The best training for climbing is to climb. However, don't start training in hilly terrain until you have accumulated 1,200 - 1,500 flat miles. Then start on short hills and work your way into longer and steeper climbs. All early season hills should be done with a steady rhythm rather than jumps. Don't jump, slack off, jump again, etc.
A technique I like when I feel ready to start forcing the pace is to ride easy until the last quarter mile, then go hard to the top. The next time I ride that hill I might go hard for the last half mile, then the last 3/4 of a mile.
My advice - and this is what I practice myself - is to start a hill with as slow a pace as possible (or as slow as you are allowed if it is a race). This will let you get accustomed to the rhythm of the hill and to breathing with that rhythm. The breathing of climbing changes totally from on the flats, regardless of how hard you have been going.
Climbing requires a body rhythm and a pedaling rhythm as well as a breathing rhythm. It all has to be synchronized. You develop the feel for it by doing it in training.
If you want to specialize in climbing or try to improve it, train in mixed terrain and emphasize the uphills.