First thing's first, count the number of shifts in the right hand shifter. Push the big thumb button in all the way a few times until it's in "easiest gear" and then put tension on the cable coming out of the shifter while clicking the smaller button (might be thumb or index finger depending on the shifter model. Count the clicks and add one.
If you are upgrading from a 7 speed rear to an 8 you will definitely need a new cassette. You will probably also need a new freehub body. If your bike is 7 and it is running a freewheel, you will probably need a whole new hub which depending on the quality of your wheel, you may just want to replace the whole wheel. You really should read this to figure out what you currently have:
http://www.sheldonbrown.com/free-k7.html
Then you can decide your upgrade path, good thing to read:
http://www.sheldonbrown.com/k7.html
If you are going from 7 to 9 you will need a new chain too, and possibly new derailers.
Unfortunately your old system, being 7 speeds, is getting on in age. Nothing inherently wrong with the design of it, but things have changed and parts have changed along with them ;-)