"Burning" effect happens when you get a sufficiently high power per unit area. So what you need is a source of power, and a way to get all that power on a small area.
In good sunlight, you can use a magnifying glass to get this kind of burning effect quite readily (wear sunglasses - you will be looking at a very tiny hot image of the sun if you do this right...). Move the magnifying glass until the image of the sun is a small bright spot, and you can set fire to wood (not just the tops of matches which burn at much lower temperature). Move the sun "out of focus", and the spot gets bigger. Now since the temperature you can reach depends on both amount of power and the size of the spot, the temperature will be smaller.
Lasers are particularly good for burning because they are collimated - that is, the beam is nearly parallel. As a result, it is possible to focus the energy into a very small spot. Which means lots of heat.
If you have multiple lasers, you need to come up with a way to make their beams focus onto the same spot. You can do this by making sure their beams are exactly parallel, then focus them through the same converging lens.
Assuming you have created a rig where you can hold the pointers still, but where you can adjust their direction, you can simply point at a far away wall and make sure the four (or whatever number) dots are the same spacing apart as they were when the wall was very close. Then put a lens in front, and focus.
Note that lasers are coherent - this is a special property that leads to relatively large amplitude. But when you have two different lasers, they will typically not be "locked" and so their amplitudes will add in quadrature (power adds linearly). So assuming you do the optical alignment carefully, you will see four times the power when you align everything carefully.
You may be interested in this earlier answer about focusing sunlight with a large mirror in order to heat things up, and this answer about how hot they might get.