In reply to Kelloggs77:
Finger strength is of primary importance in climbing and a lot of technique is essentially to load the fingers as little as possible so you can execute moves or conserve finger strength for further moves.
As you probably know there isnt any muscle in the fingers themselves so the strength is in the forearm muscles. These are relatively small muscles and so gains can be slow. As they are small CV fitness is not useful even for endurance routes.
The first key thing to realise is that the fingers don't move on the holds (usually) so the strength is isometric. Isometric finger strength is unique as a primary performance factor compared to other sports and less is known or has been researched as a consequence.
Max grip strength and finger endurance are also both important. The first more vital for bouldering and the second more important for (non-cruxy) routes.
There are two types of strength gains you can elicit. One is neural based which trains existing muscle to work more efficiently and the other is increasing muscle sze (hypertrophy). The neural gains can lead to quick and rapid results and then plateau leading some to lose faith with fingerboarding as further gains are much harder to come by.
Fingers are surprisingly robust for such small structures but the type of work climbers do mean that tendons and other supporting structures and attachment points do get pushed to, and beyond the limits.
Fingery bouldering should be your main tool to improve max finger strength and intervals on bouldering circuits and routes for increasing finger stamina.
A secondary classic way to improve finger strength is regular deadhanging from fingerboards. As finger strength gains are typically slow I see no reason why a beginner shouldn't make a habit of this from the outset if they have any ambition especially as it can be done at home.
When deadhanging try to use a variety of grips so you get good on slopers, drags, half-crimps and crimps. Spreading the load will help prevent injury too.
Stop strong, stay hydrated, be mindful of small pains/tweaks.