I would suggest watching Richard Dangles on Youtube. He has good guides. But I'll go ahead and tell you how I personally play him.

Demolition's main role is killing Fleshpounds. He can also kill Scrakes, but is not the "main" perk to do it and can sometimes be risky. He's also good at clearing crowds of trash Zeds with his explosives.

For skills, all left side skills is usually what I use. You can also use the Right Level 5 and 20 skills if you wanna sacrifice damage for knocking a Zed down.

For the main weapon, RPG is the easiest one to use. There's also Seeker 6 and M32 which fit other roles, but if you're just starting out, I suggest sticking with an RPG until you learn Demo's mechanics.

With the RPG, you can easily kill Fleshpounds with a few rockets. The number depends on level, difficulty, number of players, and where you actually hit it. But I never used more than 4 rockets on a single Fleshpound.

Quarterpounds are even faster to kill. If you see these guys with a Fleshpound, I suggest taking them out first. I don't remember ever taking more than 2 shots to kill one QP. Most of the time I even kill multiple of them with 1 rocket.

For both FP and QP, you should aim for their chest core. It's the yellow thing in the middle of their chest. That's their weak spot. The Fleshpounds block it when they're angry so it's easier to hit it when they're calm.

The Scrake is resistant to explosive damage, so blowing it up isn't as effective. The best way to take these guys out is using duds. A dud is when you're too close to your target so the grenade or RPG don't blow up. If you get close to the a Scrake and shoot it in the face with your RPG, you can kill it. With all left side skills, you can even one shot them this way.

Just be careful when you're in a team. If you have a Sharpshooter, Gunslinger, or even Support and Berserker, you should probably leave the Scrake for them. If you do attempt it, make sure your teammates know you're going to because they might start shooting it and make it move around too much, causing you to miss. Or you could also end up blocking the Sharpshooter's Railgun.

For a second weapon, you can use M16 or M79. M16 is good because it let's you protect yourself from small Zeds while letting you shoot some grenades. M79 is good if your team is camping together and someone is watching your back. You can just keep shooting groups of trash Zeds to clear them.

Personally I don't use the M16 anymore, and I rarely use the M79. I've switched to MP5 or HM201 as my second weapon, but that's just my preference. Reason is that way, I get some extra space to upgrade my RPG. But since you're just starting out, you should try M16 and M79 first and see if they work for you.

Also another tip is that Demo's grenade is half a stick of dynamite. If it lands on the ground, it takes a long time to blow up. But if you land it on a Zed, it blows up instantly. Not only that, but it also makes the Zed that survived the blast stunned for a few seconds. It's a good opening for when you wanna kill a big Zed safely. Stun the Fleshpound and then blow him up. Or stun a Scrake and shoot a rocket on its face.

This is the weapon progression I follow in a Survival match:

On the first wave, I usually try to group small Zeds together so I can clear them with one shot from the HX25 Grenade Pistol. If I have any survivors, I just Bash them to death or add them to the next group that is going to be blown up. I try to save my 9mm ammo on Bloats since they don't blow up easily. The only thing you gotta watch out for is corners, since you can't really clear groups that fast, only being able to shoot once every reload. Getting trapped in a corner is rough for Demo.

After the first wave, I buy a gun depending on how much dosh I have. If I have less than 700, I usually just buy another Tier 1 gun and buy a little ammo for my HX25 Grenade Pistol. Usually I grab the AR15 since it's good enough to defend myself with. I've seen a lot of people buy a Tier 2 weapon right away with 700 dosh, and they end up running out of ammo after like 3 minutes. A good gun is worthless if it's empty.

If I have more than 700, I buy a Tier 2 weapon. If the HX25 still has ammo, I keep it with me just in case, but I usually don't refill in the trader and instead let it refill with ammo boxes.

I get the M79 if my team is just camping and they can protect me from anything that gets too close. If the Medic is having a hard time, I grab the HM201 to help with healing and killing smaller Zeds that are too close. If I'm soloing, I grab the MP5 and use that for moments when the HX25 isn't enough.

Just before the wave Fleshpounds start to spawn, I try to get the RPG. This is the point when I finally sell my HX25. If I don't have enough for the RPG and my teammates don't wanna share money, I sometimes end up selling my Tier 2 gun too, but that's rare. And when you get more Dosh, you could also swap out the tier 2 gun for the M16. With the RPG and a second weapon, you should be able to finish the match.