If you think you can do it,which I'm sure you can, here goes.
Turn off the water to the cistern and flush toilet.
Plastic one:
Remove the float off the arm it unscrews. Remove the arm from the Valve assembley by squezing the plastic pin end pull the pin out and the arm will drop off. Undo the large knurled plastic nut and remove the pin and washer. Replace with new washer same pin in reverse order refit the arm and float job done. Turn on the water.
Old brass type one.
With the brass type it has a barrel inside the valve housing.
Remove the float. Remove the valve body end cap.
Remove the split pin holding the arm to the valve assembly.
Gently ease the arm down until the valve barrel pokes out then remove the arm. Pull the valve barrel out that has the washer in it. It's easier to buy a complete valve barrel , as they are buggers to get apart to put new washer in. and a new BRASS split pin for the arm. Don't use steel it'll go rusty.
Replace in reverse order. Check the arm end fits the slot in the barrel.....Put a thin smear of vaselene on the barrel it'll make it go in easier, make sure when you put the barrel back the slot is at the bottom as the slot takes the funny shaped tip of the arm. Refit end cap refit arm and float turn on the water. The trouble with the older valves there is no adjustment other than bending the float arm down so it turns off sooner. Some times you have to fiddle around with the arm to get it back in but it wll go. Don't forget to slightly bend the split pin to stop it coming out in use.
Hope this helps. Go on you can do it.
If you think you can't phone your local council and ask if they have recomended tradesman list, some do. Or citizens advice.
Nobby, March 2008