Honestly, just boulder more and the strength will come.
A lot of the usual grip based exercises don't really have a good carry over into rock climbing / bouldering because of the nature of the holds you use. Something like crushing strength (the type of strength you use when you close a hand gripper or shake someone's hand) isn't much use when you're using your finger tips to pull on a half inch hold.
Since you stated you've only recently got into it, I'm going to address a few different things.
1) Adaption - Depending on what you mean by recently, chances are your forearms are still adapting from not doing much to having to support you hanging your bodyweight from your fingertips. Unfortunately, there's not really a fast way to get over this, just trust me, it'll come with time (though you will climb harder as you get stronger, which will put more stress on your forearms, so you'll probably never completely lose the pump / ache, you'll just learn to handle it better).
2) Technique - As a guy (assumption based on your username there) and someone who's only recently discovered the joys of climbing / bouldering, I'm going to assume that you're doing what most guys do until someone points it out to them and relying on your upper body / pulling strength a fair bit. Most guys, without really realising it, take the "see hold - pull on hold" approach, which will get you through easier problems, but if you want to progress to harder stuff (and save your grip burning out too soon), you really need to look at your footwork and position.
I can't write a detailed explaination without seeing you in action on a particular route, but watch what other people are doing (more experienced ones) and how they're moving their body and placing their feet. Particularly women as they usually don't have the upper body strength to rely solely on aping up routes using their arms.
More feet and better body positioning = less pulling with your arms = less forearm pump / burn out.
3) Tendon / ligament strength - One of the main injuries seen in boulderers, particularly newer ones, is pully injuries (tendon / ligament pulls). This is because your fingers aren't used to holding your entire bodyweight, and your muscles strengthen faster than your tendons / ligaments do. Unfortunately the only real way to strengthen them is time. You can do fingerboard work (go easy though) which will help, but don't do it at the expense of actually bouldering and working on your technique.
This is also one of the reasons I wouldn't go nuts training your forearms with a whole host of different exercises... it's perfectly possible you'll get your forearms stronger without your tendons / ligaments keeping up, and pull something.
4) Core strength - For a lot of bouldering problems, particularly when you get into overhanging ones, you need some crazy core strength to maintain a good body position. When you're climbing on the underside of a roof, it's much more efficient to brace yourself between holds with your feet and heel / toe hook where you can, than it is to treat the problem like a kid on money bars; for that, you need a really strong core.
5) Stretch (gently) and work your extensor muscles - given all the above points, to help with recovery, you can do some gentle forearm stretches (watch some yoga videos, but seriously, take it gently, I've watched a friend of mine seriously pull a tendon through stretching his forearms too aggressively). You can also get an elastic band, wrap it around your finger tips with your hand in a duck bill type position, and open your hand so your fingers are spread. It should work the muscles on the outside of your forearm, which will help maintain a decent balance of strength, and assist with recovery.
Getting the blood flowing to your forearms is also a good idea, pretty easy to do, just go from a fingers spread position to a fist several times, like when you warm up before a session (you are warming up first, right?).
You can also get a squash ball and roll it between your forearm and a desk / the floor for a bit of self myofascial release, be warned, it hurts.
To sum that all up (because I always get carried away when writing about climbing), 1) give it time, 2) work on your technique and don't rely purely on strength, 3) give it time, 4) work on your core strength (climb like a woman, though possibly not Alex Puccio) 5) stretch, work your extensors, get the blood flowing and don't forget to warm up.