You'd probably want to replace the counter top, something that is easily done. You can buy prefab counter top at any of the big box hardware stores. Then it is just a matter of cutting to correct sized hole for the new sink, which you can buy at the same place. If they don't have the size you want they can order it. You can reuse a faucet or get a new one. Then you'll need re-plumb the drains and water supplies.
Depending on how 'handy' you are it is a weekend or two job. You'll need at the minimum a saber saw:
link and a drill
linkAnd a some plumbing tools