First, take off all the doors, drawers and counter tops. Many times, counter tops are glued to your base cabinets, and are bolted together at the seams with pocket bolts. Try to take these off carefully if you plan on re-using them, or donating them too.
Then, look for a board near the top of the base cabinets, this is the board usually used to screw the cabinets to the wall. Take the screws out that are being used to secure them to the wall, and it's likely that they'll can just be pulled away from the wall. Be careful though, sometimes, the base cabinets are screwed to each other too, so look at the insides of the base cabinets to see.
The same basic process can be done for the upper cabinets as well, except that you should make sure that they are not screwed to each other before trying to take one down. This is almost always a two-man job.
As for donations, I suggest looking for a Re-Store in your area. They are operated by Habitat For Humanity, and I personally have purchased many things (including cabinets) from them. All the proceeds from the sales of donated items goes to help low-income families earn the pride of home ownership!
I would handle this as a tile countertop. Instead of small 4x4 tiles you will be working with the larger slate sheets. This means, 3/4 plywood down as a base. Cement board on top of that and then thin set to attach the tiles.
You can then trim the outsides in whatever you want. It can be wood, tile or metal. You can also use the slate cut into smaller pieces to trim as well.
Once everything is set, you should then use grout to fill the gaps between the slate sheets.
Remember, just like tile you need a good solid base; so skip the MDF and use plywood.
Best Answer
In my opinion, wood is a very poor choice for kitchen counter tops. Any wood is dimensionally unstable to some extent, how much depends on several factors such as moisture content during installation and method of construction. It can be relatively stable or a complete disaster.
My main objection is wood is porous. Ideally, kitchen countertops should be impervious. Most materials have pores to some extent, but they should be as microscopic as possible. Wood pores are relatively gigantic. While oiling is helpful, wood will get stained from food and other products that come in contact with it. Some may say this gives it character, but to me, it just looks unsanitary.
Speaking of sanitary, despite the moniker 'butcher block', meat should never be processed on a wood surface. It is impractical to properly sanitize wood in the home. Chop all the fruits and vegetables you want on it, but only cut meat on a dedicated impervious cutting board that can easily be sanitized.