How do I count the number of songs uploaded to iTunes?

Ah, you mean the Status Bar. Either:

• click on iTunes' top bar menu: View/Show Status Bar
• use the shortcut command: CTRL+/ (that is, hold down the CTRL key and the forward slash key at the same time)

Once it's displayed, if you click on the Status Bar text, the information will toggle between:

• the number of songs, total running time in days:hours:minutes:seconds, size of library
• the number of songs, total running time in days, size of library

Upon re-reading your post I notice that you wish to see these numbers before Sync.

If you use Sync entire library, it will be the size indicated on the Status Bar. If you use Sync selected playlists, albums artists and genres, the size will change as you set which items you wish to add to your iPod, but the number of songs will be indicated on the Device/Settings/Music pane where you decide which songs you want to add. I don't think you can determine the actual size at that time though:

You will find that information on your iPod.

On a 6th generation iPod Touch for example, go into Settings/General/About and you will see a section on that page listing the total number of songs, the total number of videos, the total number of photos and even the number of apps you have added. On other generations of the Touch it will be a under the same, or a very similar heading.