What Muscle Groups Should I Train To Make Bicycling Uphill Easier?

jhuskey said:
I know this is not what you want to hear but do more climbing. Eat right, sleep well and your body will figure out which muscles to target. Weight lifting is a great thing but is not what you need to be great climber.

Pretty much. A good balance between practice, rest and nutrition is the best to achieve results. Climb, and you'll climb higher. :)
Strong quads and good calves muscles are a must, you are not only pushing, but also almost standing when going uphill because you are going to to be kicking, and using those calves to really get the most of each rotation is very important.
Hamstrings and glutes over quads and calf muscles.

Think about what quads are supposed to do and how they don't really get to work in that range of motion on a bike.
MingMeng said:
Everything's fine, but when I start going uphill, my leg muscles scream in agony! .

The funny thing is, the hill I'm trying to get up isn't even steep.
Hills are different than flats. There is no coasting on hills. If you are not comfortable with your legs screaming in agony, use a lower gear and don't work so hard.

No matter how well you train or how strong you get, you can still make your legs scream in agony.