Normally, I have both the right and the left hand as here
The left hand stave was always missing in that book of piano sheet music I saw yesterday, however it had letters above the stave for right hand just as in the picture above. Both the shopkeeper and the title of the book said that it was for piano and the songs were not for beginners.
Where did the stave for the left hand go?
What are the letters? Are these cords, as discussed here?
Correct, those are indicative of 3 note chords (generally the base / root note, plus the third and fifth above that note). These three note chords are also known as Triads.
This is probably for improvisation purposes, as it gives you the melody in the right hand, then just the idea of the chordal-pattern in the left hand - so that you can do with it whatever you like (as long as it fits within that chord).
In the above sample, C - A - D would be the chords consisting of
Edit: To clarify what is on the link in your question, the three variations are called Inversions. They contain the same three notes (C-E-G), just in different orders. There are names for the three inversions (that I don't see mentioned in that linked page):
As far as when you should use them, that might be complex enough to constitute it's own question. You can experiment to see which one fits best in what your playing.
It's generally known as a "Fake Book". Meaning it should give you enough information to "fake your way" through the song at a birthday party or something.
Also the chords are usually in Jazz-Guitar syntax. It's similar to figured-bass. But you're not going to see G 6/4 or any thing like that. A G6 has an E as well as a D. A 'sus 2' has a 2 instead of a 3. Same with 'sus 4': no 3. If it says 'add 9', do that: just add a 9. But if it says just G9, you need a flat 7 in there too (Jazz chords often just keep adding thirds off of the triad, so G11 has a flat 7 and a 9 picked up along the way).
[ This is why you'll hear guitar players say: "Don't play a 6/9, play a 13-no-11!" It's because you have to drop the 5 anyway because you run out of fingers! This bit may not be "good advice" but my experience is that you can "get away with it". As @Gauthier has commented, this way of looking at it doean't give you the right seventh. ]
A chord like C/G is a second inversion: it's a C with a G at the bottom. A/G is an A7 in third inversion. These are usually indications of a moving bass-line. The bass needs to lead the harmony into the next chord.
There should also be a chapter or at least a pattern index of ideas for the left hand. Otherwise the book is really leaving you hanging. Off-hand some ideas are: block-chords on the eighth notes (Jerry Lewis boogie-woogie), simple Mozart arpeggios, broken chords as accents (pretend to be cymbal crashes). There's a great book called Boogie-Woogie Hanon that's an excellent resource for left-hand blues-rock patterns.
It's not quite correct for the shop owners to stear you away from that type of sheet music because it's "not for beginners". It sounds like most of your musical training is in reading that type of music but many musicians start start by reading chord and single-staff music like that. You just need to learn a little bit of theory like what was mentioned in the other posts above. As your theory and improv skills grow the complexity of your left hand accompanyments grows just like how you start reading sheet music with simple scores and then move to more complex ones.
If you are interested in jazz theory (it's not as hard as it sounds!) I recommend you buy the book titled "The Jazz Piano Book" by Mark Levine. I got that book when I was 16 a year after I started playing piano and it changed my playing forever.
