Just do it, don't aim too high at the start, avoid the smaller holds too soon stick with the easier climbs to get the technique, hand strength will come naturally with time, bad strains from overdoing it can really stick around especially when learning.
Legs are an important part at least as your arms, but technique will help both last longer.
I was no pro at it, all I did was a lot of climbing, and various pull ups on various sized hang boards/campus board/holds.
I'm hoping to get back into at least indoor climbing in a couple of months
I miss being able to do pull ups with two fingers on each hand (one when drinking at the bar)