use the time shift tool to line up the second file right at the point the first ends, listen to an area near the end of the first and beginning of the second, delete any gap, then save, with the two files now becoming one. Correct?
No. What you're doing is "Export", not "Save". "Save" means save the Audacity project.
Here's what I do.
Import the MP3s
Line them all up on the same track. They are now
separate clips on the same track.
Delete the silent gap between songs. You now have multiple clips on one track, and each clip is a complete song without the annoying silent bits. (See before and after images at bottom of this post)
Double-click on each clip, do Tracks > Add Label at Selection: type the name of the song in the label
Do File > Edit Metadata and enter the Artist Name and Album Title information, clearing all other fields.
Do Edit > Preferences, go to the Import/Export tab and uncheck "Show Metadata Editor prior to export step"
Do File > Export Multiple. The default settings should export a separate file named according to each label.
Now, as Steve has pointed out, if you export as MP3
gaps will appear again. You can prove this to yourself by first exporting WAVs then exporting again as MP3s. Import a WAV and MP3 of the same song into a new Audacity project and compare them - the exported MP3 will have silents gaps at the beginning and end as shown below.

- WAV versus MP3 export, re-imported into Audacity
- Screen Shot 2012-02-20 at 6.10.41 PM.png (30.21 KiB) Viewed 1758 times
Also as Steve points out, if you are burning to CD, export as WAV. If you are importing into iTunes, I still recommend exporting as WAV and importing the WAVs into iTunes then use iTunes to create the MP3s. Not that iTunes does a better job, but it does it faster. The in iTunes select all the MP3s you just created and make them a "gapless album". iTunes will set some internal pointers or some such so that it eliminates the silent bits and the performance will flow as you intend.
If you intend to burn a CD, the WAVs you exported can be used for that purpose. Just be sure to set the between track "pause" in your burning software to zero for all but the first track.
Examples of before and after deleting the silent gap with songs on the same track

- Before deleting gap
- Screen Shot 2012-02-20 at 5.59.05 PM.png (11.26 KiB) Viewed 1758 times

- After deleting the gap
- Screen Shot 2012-02-20 at 5.59.27 PM.png (8.52 KiB) Viewed 1758 times
-- Bill