All the links that are provided here are for windows, if you are running Mac or Linux, you can find links to them on the main page.
first it all depends on the type of audio file your phone can play. some of the older ones use AMR and WAV but majority of the new one can play MP3. Audacity can export files as WAV and MP3. if you need it to be AMR you will need a converter. to make a ringtone, first you need audacity. the latest version is 1.2.6 you can get it here http://audacity.sourceforge.net/latest/audacity-win/audacity-win-1.2.6.exe
once that is installed, if you need to make the files MP3, then you'll need to download this http://www.webhostxpress.net/~mitiok/lame-3.96.1.zip
extract that to a folder here you wont forget it. open audacity, open the audio project, click on edit>preferences>file formats>find library>open the lame_enc.dll file that you just extracted. to the left of the find library button is a drop down menu of the available bit rats for your mp3. the lower the number the worse the quality but the less space it uses. 128 is a good compromise of space and quality where 320 is "cd quality". click ok.
now in audacity, click on project>import audio> and open the audio file you want as a ringtone. once the track is imported, you can edit it as desired for the ring tone. for example, lets say you want the chorus of a song to be the ringtone, first make sure that the selection tool is the one you are using, it looks like a capital "i", play the file, find the begining of the chorus, click the selection tool there, press play and make sure you dont have the begining of the chorus cut off or that you have extra music before the chorus. you can fine tune the position by zooming in (ctrl+1 or ctrl+mousewheel up) then click on the new location, you can also use the left and right keys to move the start point 1 step at a time. once you have the begining of the selection set, zoom out a bit (ctrl+3 or ctrl+mousewheel down), move the cursor over the line at the selection point and it should turn into a hand pointing to the right, click and drag the selection out to where you think the chorus might end, press play to hear the selection, once you have the selection set to exactly what you want as the ringtone, press CTRL+T and that will trim the track (deletes everything outside the selection) now click on project>align track>align with 0. this will move the clip to the begining of the track so you wont have silence for a minute before the song starts. once that is done, you can click file>export as wav or export as mp3, pick a file name and then you are done.
now you just have to get it on your phone, depending on your phone, you may need to link to your computer with a usb cable, use a bluetooth connection, use MS Active Sync (for phones with Mobile Windows), or you may have to send it to your phone via MMS or E-mail. check your user manual if you are not sure how to get multimedia onto your phone. if you have a memory card in your phone, and you have a card reader on your computer, you can just put the card into your computer and copy and paste it to the music folder or just in the root directory of the card.
if you still have questions, let me know. i use audacity to make ringtones all the time for my phone.