This is the beginning way for the people who don’t want to spend money.
For starters, once get to Tutorial Island, I suggest you get every possible skill to level 3 and that includes Fire-making. It will be easier for you later. Once you get to Lumbridge, bank all the items except the Bronze Hatchet and the Tinderbox.
Now go to a quiet place with a lot of trees. I suggest West of Lumbridge. There is a huge forest with loads of trees. Start chopping them. Once you are full, go to the Woodcutting Tutor. He is just a bit East from the forest. Once you are here, start burning the logs. You may take a few tries while trying to light up a log at the starting levels. But as you get your level you never have to take more than 1 try. Keep chopping and burning till level 15 Woodcutting, at which point you should have a greater Fire-making level.
Now near the Woodcutting Tutor there is a Oak tree. Start chopping it. It gives multiple logs, so once the tree is cut down start burning them, and by the time you finish the Oak tree must have spawned again. Just keep doing this till you are level 30 Woodcutting. You should have a higher Fire-making level if you burned all the logs you cut. Now go to Draynor village. To go there, just go East from Lumbridge and follow the path. It leads to Draynor village. All you now have to do is start chopping the Willow trees here. Have only the Hatchet with you as you chop. Now instead of burning, start banking. Just keep banking and chopping. Once you get to level 60, you should have tons and tons of Willow logs.
Now go to Varrock. You may want the help of an experienced player to get there or you can just see the map and go. Once you reach Varrock get to the Grand Exchange. Go to a very less populated world. Now here just take the Tinderbox and withdraw your logs and start burning them. This is very easy as you don’t have to keep moving around. Finish one round and withdraw more and keep repeating. Once all your logs are burnt, go behind Varrock palace with your Hatchet and Tinderbox. There are three Yew trees here. Start chopping them and when you are full just burn the Yew logs. These are very fast as they give 200 Experience to each log you burn. Keep chopping and burning.
You’ll get to level 99 in Fire- making faster than Woodcutting. Once you get level 99 Fire-making, keep chopping Yews and start selling them if you want more money.
Now this is for people who spend money on buying logs.
If you are very rich, I mean if you have like 30 – 40 million, I suggest you buy logs and burn them. Just keep burning till you have high enough level to burn Willow. Now, if you want to save money, I suggest you keep burning Willow till you get to level 99 as they are very cheap. But, if you wish to get to level 99 quicker then I suggest at level 45, you move to Maple logs. Then at level 60 start buying and burning Yew logs. You’ll get to level 99 in no time.