Hi Rodders, going up hills is a big ask of your body if you are not used to it. When we were training for Kili we would walk up to the top of Snaefell and back from Laxey. The first trip took us 5 1/2 hours and was brutal, we kept doing it every other weekend (also trying out different kit whilst we were up there; overtrousers, windproofs, backpacks, etc to see which was best for us).
By the 5th trip it took us 4 hours there and back (this included stopping for photos along the way).
As well as the suggestions above, I'd also suggest picking a short hill (something you can climb in 5-10 minutes). It doesn't have to be out in the wilds, it can be your local high street. Something that will get your heart racing. Do it every day, build it into your day somehow, going to the shops, to work, after work, etc. The more you do it, the easier it will become (although it may never actually become "easy"). Don't look to set a personal best on it each day, just look to get the hill done as best you can.
I walk to work every day and I build in a steepish hill, it really helps me, although having said that we were out at the weekend and climbed Cronk Ny Arrey Laa from Niarbyl, a short walk but a brutal climb, managed to make it up in one go but I was blowing hard and envying those around me who could still talk on the tough sections!