Sigh .. can't seem to kill one. Any tips? Help! :)

Which weapon are you using? I don't remember which level I was at when I defeated the Deathclaws, but I think I wore leather armour, used a Sniper Rifle and could take them down by always aiming for the eyes. Ideally I already dealt a lot of critical damage until one was close to me and then I occasionally needed some Stimpaks until they died after some more hits to the eyes.
Most importantly you shouldn't have more than one attack you at a time. I had to wait for a while until the last two Deathclaws finally walked a bit further apart so that attacking one didn't also lure the other one towards me.

Good tips. :)
So basically the eyes are the vulnerable parts? I'm trying to use the rocket launcher but I tend to get too close and blow myself up. =P
I will see if I can get a sniper rifle. Yah, you're right, if two go after you, might as well sign your will and prepare for a funeral. :)

My first deathclaw ever, I ended up throwing grenades at him. Which was a strategy that worked until Dogmeat ran right up next to him.
I will forever miss that pup.

Personally I like wearing hardened power armour, trying to be at a good distance and firing at them with a minigun.

Rule 1: Don't you EVER let them get too close to you.
Rule 2: Aim for the eyes, boo!
Rule 3(my addition to Syrion's tip): When they get close to you (they will, Rule 1 is achievable only with hi-tech weapons :D) few bursts from Combat shotgun can rip apart practically anything

That's one of the problems. As soon as I enter that section (which is the only way to get to other sections), a deathcrawler is standing right next to me. Suggestions?

If you are when I think you are (Fallout 1?), then you should be able to run between deathclaws to the other side of map, to other area. Then, when you return back, they should be at their starting positions (maybe they restart after some waiting... Just try it out), AND you should be far enough from them. Toy with it a little, you'll see, I know I had the same problem and solved it quite easily

I tried that with one more quickly running over to me... Somehow I won..

If you're coming from the Boneyard you should be able to simply rest or wait for a while. I am unsure how Fallout does it, but I suppose the Deathclaw will be at a different position next time.
My problem once was that I was coming from the Gun Runners, from the other direction that is, where you can't rest and one of the Deathclaws was standing right next to entrance. Because of this I basically didn't have a chance to go back to the Boneyard unharmed.
I loaded an earlier savegame to avoid this another time, but you should also be able to simply run away in combat mode. I'm not sure, but I think you can outrun a Deathclaw like this, but a few hits will probably be unavoidable.

i think we're talking about the deathclaws in fallout 1, in the boneyard? if you're in the boneyard, there's a quest with smitty that can get you a turbo plasma rifle, which will allow you to fire shots for only 3 APs. usually, that's enough to take out a deathclaw from a distance.
i'd only try to take on deathclaws if you have power armor. combat armor is enough to outrun them and make it to the next screen. if you have power armor, burst weapons at point blank range will rip apart any deathclaw. if you have a high agility, you should be able to get off 2 minigun bursts a round. bursting at point blank range into the eyes is more than enough to kill a deathclaw a round. and with the power armor, you'll have enough protection to survive the attacks from any other deathclaws involved in the fight.
another strategy would be to try to attack the deathclaws one at a time. you can do this by being patient, waiting for the deathclaws to separate from each other, and then by initiating combat yourself.
also keep in mind that the deathclaws will continue to reappear in that section of the boneyard, even if you kill all of them there, unless you complete the deathclaw nest quest.

Yeah, technology is the answer.
I think I took out my first Deathclaw in the Hub with Sniper Rifle shots to the eyes and maybe a blast from the Combat Shotgun. I don't think I was wearing anything better than Leather Armor. But I was cranked out on Psycho, so even though the Deathclaw smacked me a few times, I hardly felt it.
By the time I was taking on multiple DC's in the Boneyard, I had Power Armor and the BFG's - Plasma Rifle for the distance work, Gatling Laser for close in work.

I feel dumb. I didn't realize there was a mother deathclaw downstairs. Doh. :)

I'd go for power armor and a minigun or a plasma rifle. But you could go for a sniper rifle, although I wouldn't advise that in the cave after you talk to Harold (we're talking about Fallout 1, right?). But if you are a low level and low on caps, go to do the first quest for the brotherhood, get the brotherhood combat armor and get plenty of shells for your combat shotgun and plenty of stimpacks.
Good Hunting!

To summarize: Don't try it at low levels. And aim for the eyes. With big guns.