If you've never come across music notation software before, think of it as a word processor where the blank pages contain staves (those sets of 5 parallel lines), onto which you compose music by placing notes.
Unlike conventional paper-based composition, using a software package means that your music looks better and is easy to edit. Even more importantly, each note is played through the PC speakers as you position it, and you can play the whole piece (or a selection of it) any time via the built-in sound library.
Professional composition software such as Sibelius and Finale are pretty costly, but Finale also makes a free product called Notepad available. Although it's limited to allowing you to compose for only 8 instruments, it's still more than powerful enough for just about every amateur musician. You can even import MIDI files downloaded from the internet, to edit and play.
Finale Notepad is a free download from http://www.finalemusic.com/notepad/default.aspx and is a 97 MB download. It runs on all recent versions of Windows and, according to my up-to-date copy of Sophos, is free of viruses and malware.