You have gotten some good answers already, but I thought that I would add a few thoughts.
Backing up can run the gamut from a very simple process (such as a good old "drag and drop" copy of key files to a second drive) to a very complex precess (such multiple, rotating backups to various destinations in such a way that some can be kept off site). Which route you choose to go is a function of 1) what you want to backup (i.e. only user created files or the entire system); 2) why you want to back up (i.e. protect files that cannot be recreated such as photos or home movies or important word processing files or spreadsheets; or maybe you want to be able to have your system backup and running just as it was in the shortest amount of time possible; etc); 3) what potential risks you want to mitigate (i.e. hard drive or SSD dying or its file system being corrupted; malware or ransomware that could damage or encrypt files; loss of the computer/drive due to natural disaster or fire; etc); 4) how much hassle do you want to endure to get the backups done (i.e. do you want it to all be automatic; do you mind having to remember to reconnect a drive; do you mind having to take a drive to an offsite location; do you need to be able to restore files created a day ago or is a week ago or month ago OK?; etc); 5) do you mind using online services and how good is your Internet connection (i.e. this is a possible easy way to get an "off site" backup); and 6) how much money you want to spend.
For #1 (i.e. what you want/need to backup), if you want to backup just key user created files that cannot be replaced, then a very simple backup plan is possible. You could go with just a "drag and drop" copy in Window Explorer to another drive if you don't have a lot of those files. If you have quite a bit of those files, then you do likely want to consider an actual backup program. If you are looking at want to do the entire system or system drive, then you are definitely looking at an actual backup program and preferably one that can either do images or can clone the boot drive. This item can also affect how frequently you want to backup particular data. As Allan
hinted at, you don't generally need to backup system/OS files or application files as often as more personal files as they don't change as often. Even many of your personal files might not change very often (i.e. those pictures from some vacation years ago are not likely going to change). OTOH, files that are more regularly changing (such as maybe calendar files, email files, or active "work" [whether personal items being worked on or actual work files] files).
For #2 (i.e. why you want to backup), this again kind of leads to the type of backup you might want to do. In particular, if you want to be back up and running as quickly as possible, then you might consider cloning your drives, in particular your boot drive, as opposed to just doing an image. Using a clone will get you up and running faster than backing up by images...if your boot drive dies, etc, you just pop it out and put in the clone drive. So, it is potentially a matter of minutes (depending on how quickly you can swap drives), while with an image, restoring an entire drive can potentially take hours (depending on the size of the drive and speed of the drive connections).
For #3 (what potential risks do you want to mitigate), this primary deals with what you want to use for your destination of the backup. If you are only trying to mitigate the possibility of a drive dying or file system of a single drive being scrambled, then an external drive or an additional internal drive that is constantly connected is fine. If you are worried about things like malware or even ransomware, then you will want a drive that is NOT constantly connected to the computer (whether internal or external) and likely will want potentially more than one backup set that you rotate through. If you are worried about natural disasters or house fires, then you will want to be able to have an "off site" backup, which can either be in the form of using an online backup service or backing up to an external drive that you detach and store "off site" (i.e. at a relative or friend's house or maybe a safe deposit box). And keep in mind that you might be worried about different potential risks for different types of data. For example, all the potential risks might be of concern for user create, irreplaceable files, while maybe only a drive dying is only a concern for the boot drive that contains the OS and applications (assuming you have all the installer optical discs for the OS and applications, which is another form of a backup). This item can also dictate whether using something like a RAID 1 array might be an option as at least one simple layer of "backup" (ideally not the only layer of backup, but if you only use RAID 1 as a "backup" scheme, then it is better than nothing).
For #4 (what level of hassle do you want to deal with), this is very much in line with #3 in that is largely deals with what the backup destination will be, but can also deal with what type of backup you want to do and how many backup sets you want and how often you backup. For example, if you want to use an automatic backup function of a backup program (i.e. less hassle), then that essentially forces you to have your backup drive constantly connected to the computer. Of course, you could then have another external drive that you periodically connect to make a second backup and that drive could then be kept "off site", but this it more hassle. And there is frequency of backup...generally speaking if you want to be able to get a file back from yesterday that you edited today, then you are looking at more frequent backups which typically means more hassle, unless you use an automatic backup system.
For #5 (whether online services are an option), this is a potential low hassle way to get an "off site" backup, but it is will be highly dependent on how much you are backing up and how good your online connection is...and how much you are willing to trust some company with your files (whether all or some of them). If you have a very slow internet connection and have a lot of files to backup, then an online service is likely not practical. And if you have trust issues with some company "holding" your personal data files, then again it is likely not an option. I know for me, I don't trust anyone but myself with some of my data, while other data I don't mind it being on a server owned by some company.
For #6 (how much you are willing to spend), this will essentially dictate whether you might be willing to spend more money for more drives to have multiple copies, including some at an "off site" location, as well as whether you want to pay money for a backup program or try to find a free one that will do what you want. Of course, there might be other factors (such as wanting to keep the hassle factor down) that might in effect limit how much you spend.
Now, having "blathered" on for a while, I will offer forth that commonly suggested 3-2-1 backup rule. That rule essentially means that you have at least 3 copies of your "data"; with two local copies on at least two different devices (one being your computer and the other being an external hard drive, optical discs, USB flash drive, NAS, etc; and with at least one copy of that data "off site" (whether using an online backup services or external hard drive/USB flash drive stored outside of your house, etc). The idea behind this rule is that it gives you pretty good backup "coverage" with fairly minimal hassle. If you decided the follow the 3-2-1 rule, then you could do it one of two basic ways.
Option #1 would be to get two different external drives (4 if you wanted a separate drive for each of your drives your are backing up). For external drive number 1, you could leave attached to the computer all the time and use an imaging program to automatically backup your drives at whatever frequency suits you (say weekly or maybe more often). For external drive number 2, you only attach when you are ready to do a backup (likely an image backup) and you don't backup to this drive as often (say monthly or even every two months)...and you keep it stored off site after you have done the backup. This would satisfy the 3-2-1 rule. 3 copies...one on the computer, one of external drive #1, and one on external drive #2. Two local copies on two devices...one on the computer and the second on the constantly attached external drive. And one off site copy...on external drive number 2.
Option #2 would be to get one external drive for a local backup copy and then use an online service for an off site backup copy. You could have the backup service backup fairly frequently (assuming your online connection can handle it...you could set it to backup at night). Then the external drive you DO NOT keep constantly attached and just run backups manually less often...or you could leave it attached and run them automatically (the former provides a little more protection, but is more hassle). Again satisfies the 3-2-1 rule.
And with either option, you could slightly expand them a little if you wanted. For example, for both options, you could add in an additional drive that you clone your boot drive to. Along the lines of what Allan
said, you then only update/redo the clone when you do OS updates or install new programs. Personally, I do this will my boot drives for both my Macs and Windows computers. Makes it much easier and quicker to be up and running if something happens to the boot drive. I then only update the clones when I do significant OS or application updates or when installing new applications. This also allows me to revert to a previous OS "state" very quickly if Apple or Microsoft bork an OS update. In my case, I use "built" external drives (i.e I buy an internal drive that either exactly matches my boot drive or is nominally the same and put it in an external drive closure of my choice...this allows me to 1> pick the type of connection for the drive enclosure I want which is typically eSATA for my Windows computers and Thunderbolt or maybe USB 3.0 for my Macs and 2> lets me easily pull the drive from the enclosure to then put in the computer if needed as many "manufactured" external drives don't allow for this).
Hope this helps and not just a lot of "noise".