Where I live in Norway there are hardly any flat places at all and when I first got on a bike here my legs were dying a death quickly because of all the steep climbs close to each other.Thankfully they go down as well as up
Since then ive scaled (ya I think its the right word lol) up some very steep climbs. It took stronger leg muscles but also advice on the best way to tackle things.Luckerly I came into cycling with strong legs from running and martial arts. Some strength training for your legs will also help im sure.
Things I can add to this post are as follows:-
1) Get plenty of rest between steep road sessions.Dont hill or mountain climb when your legs are still sore from the last time. This is vital and not to be ignored!
2) If the area allows zig zap or crease S shapes up the hill. This technique helped me hugely and allowed me up places that I simply cannot reach without it
3) On the approach to the steep pick up as much speed as possible, change into an easier gear just before you know you really need to and be determined that you will get to the top.
4) If your fitness is failing you then use breathing techniques to assist your lungs
I hope this extra info helps...it certainly helped me when I found it.