I'm a girly by the way with lots of stamina and determination and the type who will pedal forever but I just don't seem to be getting faster on the climbs. When I push hard I get really painful leg burn almost straight away – so do I start with short, frequent intervals, on the road or offroad and do I start on gentle climbs or go for the big ones and ride it as fast and hard as I can?
I'd be looking at doing some 20 second hill sprints, with 40 seconds recovery, hard as you can from a rolling start on a gradual sort of hill, roll back and do it again. Start with sets of five. After the first set, have a five minute rest – just roll around to keep your legs moving – then do another set and repeat, so you do three sets in total. Try that a couple of times a week, then after three weeks, go to 30-second sprints with 30 seconds of recovery.
You can build power and lactic tolerance pretty quickly and that should help. I'm not a coach though, it's just what works for me and you may be quite different physiologically. If you do do that, or similar, make sure you warm up properly for around 20 minutes first including some short, hard efforts.