There are many ways to light a fire in a wood stove. There is no one right way to do it and I am sure that all the stove owners out there will have their own individual ways of lighting fires that have developed over the years.
This is one way to light a woodburner. Ensure that the stove firebox is not full of ash - remove ash if necessary using a suitable metal container. If the stove is a multifuel stove where the only air supply is from beneath the stove grate then you will need to make sure that the grate is clear from ash and that the ashpan is empty (or at least that the ash in the ashpan is not obstructing the air flow to the fire).
Open the bottom air vents of the stove and open the flue damper if you have one. Some people use firelighters but personally I think that they smell bad and are uneccessary.
Start with some pieces of newspaper and scrunch them into loose balls. Some people tie them into knots or other shapes which is fine as well. I have tried this and it takes much longer than just scrunching the paper into balls.
I use about 8 full sheets of newspaper to light the fire. It is possible to use much less paper, but if there is no need to conserve your newspaper supply then my opinion is that you might as well be assured that the fire will light by using a little bit extra.
Pile the balls of newspaper in the centre of the firebox.
Get some kindling. If you do not have some already prepared then use dry seasoned pieces of firewood. Softwoods or light hardwoods are best so pine, beech, or ash would be fine.
Use a hatchet to chop the wood into some small pieces roughly 10mm square. The sizes do not have to be very precise and I would not recommend measuring each bit! Lay around 6 small pieces on top of the newspaper in different directions - rather like the game pickup sticks. The idea is that air and flames should be able to get to each piece of wood. Now lay a few larger 30mm and 40mm square pieces on top.
Light the newspaper in a couple of places at the bottom and when they are going close the door of the stove.
Once the wood has caught alight and the fire is going well inside the stove you can put some larger pieces of wood into the firebox. Place them gently on top of the fire. Do not fill the firebox with wood - I would recommend burning around 3-4 large pieces of wood at a time. At this stage you can turn the air supply down a little but aim to maintain good flames whilst not letting the fire smoulder.
If you have air vents at the top of the stove then close down the air vents at the bottom and open those at the top. You may need to do this gradually as the fire develops.
A novel way of lighting a fire is in a top-down direction. You start with the bigger pieces of wood, then on top of them put the smaller pieces of kindling and on top of that lay some newspaper balls. Everything is done in the same way as in the bottom-up method discussed above but just in reverse order. Light the newspaper and the fire will work it's way down. Surprisingly this is a remarkably good way of lighting a fire - why not give it a try.