When I helped my friend prep for her first big ride that had a lot of climbing I had her do hill repeats with me. I have a good hill that is just under a mile and maybe 4-5%... I had her ride it up and down til she said she couldn't do any more... and then we did one more ... with me praising her and insisting she COULD do it... and she DID Yeah, it hurt, but I really believe you can always physically do a little more than what your brain tells you!

To start I had her set short term goals... such as... we'll make it to the speed limit sign and you can stop to take a drink if need be, but no stopping til then... etc...

DebW is right on the downshifting... try to keep your cadence consistent til you're in your granny gear if you need it... when you down shift while climbing you need to "soft pedal" for that split second shift so you prevent dropping your chain or messing up your chainring too... not a huge deal if you don't occassionally, but over time this will preserve the life of your components...

as you get stronger follow what Veronica said... sprint it til you can't any more one day, bigger gear one day, stand one day etc.

And CELEBRATE your accomplishment... the first time my friend climbed a big hill that is well known we all cheered at the top and insisted that she whoop at the top with us. The sense of accomplishment is deserved...