1. Anticipate the gear required for the hill, and select it before beginning to climb.
It's tough to change gears with low RPM and high pressure on the pedals. It's better to be in too easy a gear.
Else, you fall off trying to change gear at the last min.
2. Ensure your bike is up to the task for your fitness level and type of climb.
My brand new bike was not. I had to change it from 52/36 front & 11-30 rear - - to - - 50/34 front and 11-34, before I even bothered to take it out on the road.
Historically, many road bikes came with 11-28 on the rear..... At least for me (6'1", 58yr & 190lb) that's not going to happen around where I live.
3. Training is not about beating yourself to sh death.
80% of your riding should be quite easy, building endurance. 20% should be hard.
4. Consider taking a coach. For approx $150-175/month you can take a professional cycling coach.
It's worth the money just for the educational benefits alone.
These guys & Gals are extremely good at finding your weak points and limitations, then guiding you past them.
(Ask me how I know) I spent 9 months beating myself and not getting faster, coach worked wonders.
Silly stuff, you might not think of.... My usual RPM on the flats was <70rpm, now I'm at 85-92+rpm. My coach made me and it really does help!
All the best
Barry