Hi Diana -
Welcome to the forum!

There's an article by Sheldon Brown about shifting that you might find useful. You can find it at http://www.sheldonbrown.com/gears.html. In general you want to be in a gear that will allow you to maintain your cadence regardless of the terrain. So you want to use lower (easier) gears on the uphills, and higher (harder) gears on the downhills.

I probably don't need to point this out, but you did say you're pretty much starting from scratch. So just in case you need this info: lower gears = smaller chainring with larger cogs on the rear, and the higher gears = larger chainring with smaller cogs on the rear.

If that doesn't make sense - keep asking!

--- Denise