This one's easy - you'll need to have read the page on relative formula mass first though or it won't make much sense. Once you've got the hang of it you'll need a periodic table (click here to download one) and a calculator.
The first step is to calculate the Mr of ammonia, as shown in the diagram to the right. This gives you the two numbers you need to use, they're circled in red, the mass of nitrogen and the mass of ammonia.
This tells us that 14/17ths of every ammonia molecule is nitrogen. We just need to turn this fraction into a percentage. You can do this by typing 14 divided by seventeen into a calculator then multiplying the answer by 100. Note that the answer is given to 3 significant figures.
Try to work out the percentage mass of nitrogen in NH4NO3 (be careful - there are two nitrogens) and (NH4)2SO4.
The best way to explain this is to use the example of fertiliser (this is the most common exam question). Fertliser contains nitrogen, which plants use to build proteins and grow. So a good fertiliser contains a high percentage mass of nitrogen. Simples.