How is the easiest free way to determine if I have a keylogger or other spyware that has been placed by an individual and monitored remotely.
Thanks

Hi, daisybbgun

Your question reminds me of using one of those guns ...
first you "take aim", then you fire it.

Monitor your Add & Remove Programs.
View the files in C:\Program Files and note any "inconsistant with what you think should be there".
Make note of any unusual or different from previous PC behavior or performance.
Check (by right-clicking your desktop taskbar and choosing) the Task Manager.
Five tabs exist, each with a story to tell.

There are quite a few system analysis tools, also.
Most are freeware, so that qualifies them as "good answers" to one half your question.
Several listed here:
http://www.bleepingcomputer.com/forums/topic3616.html

Its the first part of your question, "easiest" that slows my answer down.
What might be easy for one need not be the same for another.

The applications such as these:
Hard Drive & System Utilites
* EVEREST Home Edition - a freeware system information, system diagnostics
and benchmarking solution for home PC users. Similar to Belarc, but much more comprehensive.
* SIW - This program performs computer configuration, analysis, and diagnostics. (Similar to Everest)
* System Spec - lets you can see, save and print a complete spec of your PC with this no-install,
system information utility and perform various windows functions.
Additional advanced info includes CPU, drives, apps, display, memory and more.

They are not hard to use, nor are they risky to any great extent.
They need to be understood, however.
They, or any downloaded freeware you install or use, can pose a risk if you fail to read the information.
Not all are "goof proof".

Also, malware of the kind you describe, may have been designed to remain hidden under the
scrutiny of programs otherwise quite fine at finding everything,
much of which even windows itself makes hard to find.

So, my answer is to post a HJT log.
http://www.bleepingcomputer.com/forums/forum22.html
Let our HJT Team specialists use their "experienced eyes" to set your mind at ease.
Let them teach you what is the foundation of careful monitoring while you
employ their specific advice.

Ask the questions that come to your mind as you do what needs to be done.
Go from there, and learn to answer your own question.
One easy step per day until you are satisfied.