just take out one of the cabinets.
They will probably be 500mm, 600mm or 1000mm wide. If you have a choice, take out the most damaged or the smallest. You can buy a new unit later, of whatever size and quality suits you.
Assess the job to see if you can do it, or if you need someone to help.
To start with, empty out the cabinet and find a torch. It might be screwed to the wall through the back; it might be screwed to the worktop, it might be screwed to the cabinet beside it. There will probably not be more than three screws. Observe the screwheads. Are the slotted or Pozidriv? Do you own screwdrivers to fit, in good condition?
Does the unit have legs? If so, they will be made of two metal or plastic tubes, one screwed inside the other. If you put on a pair of rubber gloves (for grip) you will be able to take hold of the lower part and screw it upwards slightly. This will make the unit lower so that (once unscrewed from the wall or adjacent unit) it will slide out. Just try one for now. There will always be one looser than the others, and one tight leg, due to the amount of weight on it.
Observe the worktop. Does more than a third of it stand on the cabinet you need to remove? If so, you will have to provide a support to prevent it falling down.
Post lots of pics for our entertainment further advice.