You can burn onto various materials, but most popular seem to be wood and leather. If burning on to leather then you need to use leather that has been tanned using the old method of 'vegetable tanning' as modern tanning methods use chemicals that are toxic when burned and you don't want to be breathing these in!
You need to choose a wood to burn on that has a fine grain, such as birch, beech or sycamore. You can source your own from wood merchants but it is also possible to purchase ready cut shapes online for a reasonable price that are excellent for practising on.
A heavy grain can be very hard to burn on evenly and can spoil your design as the nib gets stuck on the grain and burns more heavily than you had planned for! An example of this is shown below on one of my first attempts. The ready cut shaped wood that I chose had a very heavy grain and it was very difficult to burn my pattern on effectively!
With a nice, fine grain it is possible to achieve simple fine line lines without the heavy burning shown on the 'stripy' teddy above!
