Open your in-game bank account and withdraw a soft leather. If you don't have one, you can buy it from the runescape gold Grand Exchange or occasionally at general stores. Leather is also dropped by some monsters when you kill them.
Kill a cow or cow calf to obtain a cowhide if you are unable or unwilling to purchase leather. The animal will drop a cowhide when it dies. The best place for this is the cow farm just north of Lumbridge, or at the pasture at the Crafting Guild. You do not have to have a certain rs Crafting skill level to get into this pasture.
Take the cowhide and some gp (rs gold pieces) to a tanner. There's one on the second floor of the Crafting Guild. You can only enter the guild if your Crafting level is 40 and you are wearing a brown apron or a crafting cape. There is another tanner in Varrock, one in Al Kharid, and a members-only tanner in Canifis.
Click on the tanner. Select "Here are some cowhides. Can I have some leather?" Choose soft leather from the selection screen that pops up. A piece of soft leather will appear in your inventory and the cowhide and appropriate number of gp will disappear.
Withdraw a needle from your bank. If you don't have one, you can search haystacks at any farm and find one for free. You can purchase needles at the runescape Grand Exchange or from crafting stores in Rimmington and Al Kharid.
Withdraw a spool of thread. If you don't have any, you can purchase it from the rs gold Grand Exchange or from crafting stores. One spool of thread will sew four soft leather items.
Use the needle on the thread. Choose the leather coif from the selection screen. The coif will appear in your inventory and one of the thread uses will disappear.