Your alternator belt will either be tensioned manually or by a spring.
If manually, slacken the lock nut / bolt, slacken the pivot bolt and push the thing that adjusts ( usually the alternator ) to slacken the belt.
If the belt is spring tensioned, this is usually done by an idler pulley. Stick a spanner on the nut on the end of the pulley and lever the idler to slacken the belt.
Now for the clever bit. I assume that you are removing the alternator as it has stopped working and you intend to replace it.
Most alternators stop working simply because the graphite brushes ( not bushes ) wear out. Scrapping an alternator because of this fault is like scrapping a car because the front brake pads have worn out.
Most alternators can be simply and cheaply fixed by replacing the brushes. To access the brushes look at the back of the unit, remove a screw or two and you will find two small metal cages containing srung loaded graphite, these will be worn and no longer making contact with the rotor.
Either replace the brushes with new or do a bodge repair by obtaining some brush material ( from an old starter motor will do ) and file it to fit the cage so it buts up to the worn out bit.
Good luck,
Vince, September 2010