As everyone said, make sure you've got your Win Me serial number first. And make sure you've made a Windows Me floppy boot disk. It's been so long I've forgotten where to go in the computer to make it. Probably in the C: tools area. But you can download a Windows Me boot disk here:http://www.bootdisk.com/bootdisk.htm
This is how I've reinstalled Windows Me many times.
You didn't say what brand computer you have, but when I've worked on older HP/Compaq machines, I couldn't get into the BIOS to change the boot order. It just wasn't there for me to see it. Apparently the computer was pre-set to search the drives at startup. If it found a boot disk in the A drive, then that's what booted first. So if you're afraid to go to BIOS, try that. If it's not already pre-set, then you'll boot to Windows regardless if the floppy is in the drive because you'll probably be told to take it out. If that happens, then you'll have to find out how to get to your BIOS so you can change the boot order.
Once you get the boot floppy working the way it should, you want to choose "Start Computer with CD-ROM support". When it does this, it will temporarily change the drive letter for your CD-ROM where the Windows Me disk will be. If you only have one, then it will probably be changed to E: drive. The drivers will load, and you'll eventually find yourself looking at the A:\ prompt in DOS.
If you're not going to partition the hard drive, you can skip fdisk.
At the prompt you will be ready to format the C drive where you'll reinstall Windows. Type in "format c:", without the quotes. It'll look like this:
A:\>format c: (there's a space between format and c:). Click Enter.
You'll probably be asked if you really want to do that. Say yes and click Enter again.
Depending on the size of the hard drive, you may want to sit there mesmerized and watch it do its thing, or go get a big cup of coffee and come back later.
When it's finished formatting, you should be back at the A:\> prompt. Now it's time to install Windows. If you forgot to put the Windows Me cd in, you can do this now. Wait till the drive stops blinking and then type E: after the A prompt and click Enter. (Looks like this; A:\>E: and Enter) Again E is your CD-ROM drive, or whatever letter it was changed to.
Now it looks like this:
and you're ready to start the Windows Me setup. Type in win9x\setup.exe and press Enter. It'll look like this:
There have been times when all I've needed was setup.exe and didn't need the win9x\ at the beginning. So if nothing happens or you get a bad command message, try just the setup.exe.
Sometime during the setup it'll ask if you want to make a Startup floppy. You can skip that, since you already have one or go ahead and make it again so your friend has one.
I've never had any problems with parts of old software sticking around as acklan mentioned.