I've heard of some songs that use the abbreviations. So, is it 10 or 40 ? It really doesn't take any special trick to learn just 10 elements. Do you have a deadline ?
My suggestion : keep looking at a periodic table, and you'll soon get familiar with it. www.webelements.com has a nice one.
There's been a thread that is talking about this right now- looking for it now...got it !
Personally I just know them from having lookedand studied them for about 5 years. I can name the names and symbols and the atomic mass of the first 23 elements in order. I believe I can name the first 54 elements in order.