I'm frustrated with the current state of information and research on climbing as a sport. There are hundreds of blog posts about climbing exercises, but climbing is terribly behind other developed sports in injury prevention, overall training (not individual exercises), and knowing how to progress as athletes.
The end goal is to climb harder grades and be injury-free, but I've too often seen the narrow-sighted logic: I'm weak --> I should train --> I'll start hangboarding --> While I'm at it, I'll lose weight.
To climb harder, you need a wholesomeness of being healthy, cross-training, and managing the weekend warrior. Instead, most of us are desk junkies-to-gym rats. We're too eager for a fix-it-all routine that we half-assed follow. We're lousy at identifying our weaknesses to know what to train.
I hate to add to the stack of search results on "how to climb harder," but here it goes:
Climb more harder
There isn't a quick training fix to climbing more. Too often people climb only the style and on the type of rock they're good at, and when in a new climbing area, spend all their time projecting a couple problems. Suck it up and climb 3 grades lower than your norm and build a solid technical base. Climb volumes of problems 2-3 grades lower than your hardest. I used to be batshit terrified on V1 slab when I was climbing solid V6. It's improved, and so has my overall ability to hop on new styles and climb well. You'll start sending your max projects faster.
[Projecting a 5+/V2 offwidth boulder in Font. I have no photos of myself on slab, probably because I'm screaming at Jeremy to spot me.]
The second part is mental: climb harder. Jeremy used to tell me to "just pull harder." Yeah, it's as frustrating as you'd think to hear that, but it's true. Think you're actually climbing hard a lot? Climb more, pull harder.
[pc: keith share. Pulling harder on The Cutting Edge, V6 Squamish]
Jeremy and I have prescribed to the 45min warmup for years. Pulling on V8 in 10min after sitting all day is asking for injury. Get seriously warm first. We normally do 3 V0's, 3 V1's, 3 V2's, etc. up until out project grade. Don't have enough time for that warmup? Well...it comes with the territory. Climbing is hard on your body so treat it well.
Increase Overall Fitness
I didn't grasp how much overall fitness level boosts your base climbing ability until I did sessions with Team of 2. The desk junkie-to-gym rat boulderer doesn't build a solid fitness base. Mostly always true: boulderers are lazy (screw that endurance stuff) and we're typically not great at other sports. Cycle, row, run, play ultimate frisbee, whatever. It'll give you a really solid cardio base and will teach your body to move and engage muscles together at the right time.
Strengthen Core and Posterior
Climbers have an extreme revulsion to squatting, deadlifting, and anything that could add weight. But so often climbers can crimp on overhanging fingernail edges, lock it off, and next thing their butt's sagging and their feet come off the wall. It's hard to gain significant weight from weightlifting, and the overall benefits far outweigh (hah!) the weight gain, especially if one of your goals is to climb healthy for years. My favorites: squats, deadlifts, levers, kettlebell swings, suspension trainer.
There's a ton to be gained by training the right muscles, but too often "training" is synonymous with just hangboarding and weight loss. They're few and far between, but a good climbing coach and trainer can point out your mental and physical weaknesses. Once you know what to work on, Google on--there's a ton of info about specific exercises.
Commit to Training
If you're going to really, honestly train, it takes a lot of time. It'll take 3+ hours a session to really build strength, and months to do it. It's not something to be done when tired at the end of a climbing session. Make a plan for each workout and log your results.
Hangboarding gets a lot of undue attention. There's a place for building finger strength, but I really think the weakest link with most climbers is instead overall fitness, core, or mentally climbing harder, and focusing on those will yield more results than hangboarding.
Despite that, the arguments between whether to do single 10sec max weight hangs on 3/4in holds with 3min rest for 3 sets vs repeaters of 7sec on / 3sec off for 10 reps with 3min rest for 5 sets...seems ridiculous, but that's due to a lack of actual research on climbing. I've done both types, whatever feels right to keep me motivated, and after 9 months of 2x/week hangboarding with no climbing, came back with solid V8 fingers. Then again, I'd rather have spent that time climbing on crimpy problems.
Most all other sports are well versed in eccentric exercises for strength gain and tendon rehab. Eccentric exercises are when you weight a muscle while it's lengthening, so that's like campusing down or lowering controlled slowly into a squat vs letting gravity drop you down. Tendons respond to eccentric movement by laying down more collagen; it's well known to heal Achilles tendon injuries in runners, and I did an intense 5-month program for my hamstring before they took it as an ACL graft. For climbing, I've been adding eccentric hangboard exercises by starting in a full crimp and lowering down to an open hand slowly over 10sec. Start by taking weight off, then add weight.
In short: do non-pulling movement. Pushups, dips, reverse flyes, wrist curls up, shoulder presses. Makes your joints feel well-oiled and less achy.
Change it up
Try new exercises like dumbbell vs barbell rows and variables like set:rep ratios. I get bored after ~3 weeks of doing the same exercises, and your body gets acclimated too. Changing it up keeps it interesting, lets you learn how your body responds to new stimulus, and forces your body to adapt. You'll have a much better innate knowledge of yourself and your weaknesses.
Now that you've read this far in this essay, I'll say what I tell myself after reading too many blogs: just do something new and get out of your comfort zone. Be smart so you have your whole life to climb.