Skiingcrazed

I signed up and am training for my first sprint tri in August. My father's friend gave me his 1991 Bridgestone RB2. I am totally new to riding (aside from gallivanting on my beach cruiser).

I am having a lot of trouble on big hills. I think most of the trouble is that I am unsure of how exactly I should be shifting. I am unsure what gear is what on this bike and what gears I should be in when.

Any advice or tips? The majority of the race course is long steep hills that I find myself walking up (so embarrassing to admit this).

Thanks in advance!!