Getting yourself up vertical walls is not an everyday practice for most people! So, training for rock climbing will also need some specific focus. This blog post about training for rock climbing and using pilates and yoga is worth a read. This recent page, written by Harry Grove of PT on demand also provides some great information.
Actually going climbing is the best training for climbing. The muscles used and the movement is really hard to replicate so if you can, just get out there. However there will be times when additional training is needed. Either you hit a plateau and so need that extra something to boost your performance, or, more likely, work and other commitments stops you from getting out and actually climbing.
As a beginner, the training you do for climbing will depend on how fit you currently are. Choose your level for more advice:
If you can’t actually get out onto some rock, a ‘fingerboard’ is a great way to keep your strength up whilst stuck inside. They’re also quite cheap. So you just need to get permission from the relevant authorities (boyfriend/girlfriend/husband/wife/landlord, etc.) and get stuck in!