1. The handle is fitted to the spindle (which you can't see) on splines, and fastened in place with a screw. Provided you've taken the screw out of the tap handle, it is just held on with lime-scale / corrosion.
2. You need to get something "U" shaped behind the four ends of the handles and tap it forward. Madrab has suggested using a partially opened adjustable spanner, which is ideal.
3. Once you get the handle off, you will need to remove the shroud. This is the chrome plated, circular, metal cone immediately behind the handle. Your's looks as if it may have spanner flats on its back edge (nearest the wall). If so, adjustable spanner again. If no flats, rubber gloves or a "Boa Constrictor" type rubber strap tool to remove.
4. With the shroud off you'll find a fairly large hexagonal nut forming part of the tap works, close to the rest of the body of the tap. Undo and you'll be able to change the washer. If quarter turn taps there will be no washer and you'll have to change the cartridge.
All "undoing" means turning anti-clockwise as you look end on from the front.
Make sure the hot water supply is isolated.