Assuming that you have the required electrical outlet and you connect both the water and drain lines per code, you are correct, it is as simple as that.

the "hole" to drill in the sink cabinet is at the top of the cabinet, near the counter. You can also cut an opening. It does not have to be a hole.

This is the height you will need to make the drain hose go high before it goes down to connect into the sink drain pipe. It's called a "high loop". One other method is to have an "air gap" above the counter. These are the two alternatives you have. The drain hose must go upwards in either case. Web search the terms if you have questions.

Okay. Not sure about electric. There are outlets above the counter, but there needs to be one below the sink? I just wanted to make sure it was possible before going any further with the plan. Thank you!

To see how much electric current they draw, look at the specs of DW's. Look online. PDFs.

You need a circuit, not a plug. A circuit from anywhere other than from the above counter circuits.

What you need is a dedicated 120v 20A circuit

It is pretty unlikely that there is a nearby circuit that you could legally tap to run a dishwasher off of. It is a pretty big current draw and there are very specific rules about electrical in kitchens.

You most likely will need to pull a new wire from the electrical panel up to the cabinet. You also need a disconnect within site of the appliance. That can be a switch or a plug. (many dishwashers don't come with a plug, so you may have to buy one separately if you go that route)

Also, by "drilling a hole in the sink base", I hope you mean drilling a hole in the base cabinet. If so, yes, that is what you do - near the top. You'll need to buy some new drain parts for your sink though. They sell little tail pieces with the dishwasher drain connection built in. It is unlikely your sink has one already if you don't currently have a dishwasher.

jilljohn i forgot to write out that the Electrical forum is the best place to continue this discussion. Believe nothing about electricity until you have gotten answers over there. Believe none of the answers above, not even mine. This is serious, not a joke, not funny. The answers above are all good, in a sense, but they all need more work too. A forum for Wiring + Electricity is where you get comments that sculpt the answer for you.

Here is a link that might be useful: Electrical forum + wiring

"Am wanting to replace an 18" cabinet at the end of the run with an 18" dishwasher. "

What is going to support the end of the counter?
The DW will not do it.

You will also need an end panel to cover the side of the DW.