What you Need
What to do
Wait for a sunny day, and pick a spot which isn't very windy.
Pick a sheet of newspaper with as much ink on it as possible.
Scrunch it into a ball with a nice area of black exposed on the outside, and put it in the tray.
Move the lens over the newspaper and move it up and down and twist it until you have the smallest spot possible focused on to a black bit of the newspaper.
Keep the spot focused on the surface of the paper, if a hole starts to form keep the spot inside the hole.
Obviously, this will get very hot so don't touch it, and you are setting fire to something so don't put your fingers near the focus point and don't do it inside!
What may happen
With any luck and a large enough lens you should be able to get it to catch fire.
Why does it happen?
A magnifying glass is a form of lens. A lens is a piece of glass (or similar material) which is carefully shaped so that all the light from a point on one side is focused down to a point on the other side (see the camera obscura experiment). Light starting off from lots of different points will end up in different places forming an image.
If you are making an image of the sun the same thing happens, but because the sun is over 100 times brighter than everything else in the image and all the light from the sun hitting the lens is focused into a small spot, this spot will get very, very hot!
Why is the colour of the paper important?
An object is the colour it is because of how it reflects light. A blue object will reflect blue light and absorb the rest - this makes it look blue. A white object will reflect all the colours very well and hardly absorb anything, so very little light is converted into heat. A black object on the other hand will absorb all colours very well, so it will heat up very efficiently.
Why does the shape of the paper make a difference?
For something to burn and keep burning, you don't just have to heat it up hot enough to burn and provide it with some oxygen, you also have to make sure that it is producing more heat by burning than it is loosing, otherwise it will rapidly cool down and stop burning. A flat sheet of paper can loose heat in all directions so is very unlikely to be able to sustain burning, a crumpled piece of paper on the other hand will tend to have a hole charred into it by the magnifying glass. This hole is quite well insulated by the paper all around it so it will stay hot, and the chances of it keeping burning when you take the magnifying glass away are much better.
Why is newspaper better than writing paper?
In order to make writing paper smooth it often has a lot of china clay (a white clay) added to it. As clay is essentially rock, it doesn't burn very well, and it stops oxygen from getting to the paper fibres. For newspapers, they use much cheaper paper without the china clay, so heat and oxygen can get to the paper fibres, and newspapers are much more flammable.
How is this useful?
Apart from being useful to campers, and a problem for forest wardens (bottles of water left in forests can act as lenses and cause fires) this principle of concentrating the sun's heat can be used to generate electricity. Mostly we use parabolic mirrors (see below) rather than lenses, as they have the same effect but are a lot cheaper for large areas. These mirrors are used to focus the sun onto a tube of water which boils and is then sent to a steam turbine to generate electricity. Alternatively, light is focused onto one end of a Stirling cycle engine which will turn if there is a temperature difference from once side to the other.