1. Look for repetitive code.
By this I mean code that occurs in several places and is mostly the same in all those places.
Reducing repetition is the easiest way of making code shorter. Start with the worst bits you can find and your program will look slimmer in minutes!
On top of that, repetitive code is bad for several reasons:
-Repetitive code is long code. Long code is sometimes easier to write than short code (thanks to copy and paste) but it's harder to read, fix, and extend.
-If you discover that the thing you have repeated contains a bug, you'll have to fix ALL the occurences of the bug.
-Similarly if you want to add an improvement you may need to add it in twenty places (or however many).
-If you forget to change something or mistype something in just one place, it can be hard to discover the problem. The bug may not manifest very often and when it does it can be hard to track down because there is so much boring, repetitive code around it.
The challenge is to figure out how to deal with the little bits of it that change between one pass and the next. More on that presently.
2. Use loops to your advantage.
You haven't used any FOR-loops in your program. They would be very helpful, especially for dealing with arrays.
3. Use SUBs and FUNCTIONs to your advantage.
You seem to get the idea. One day you'll need to learn the principles of good modular design but I don't think it's time for that right now.
4. Use arrays to your advantage.
The real power of array lies in using variables or expressions in their subscripts. You've been doing things like
IF cardTotal(1) <= 0 THEN card(1) = 0
but you don't seem to have realised the AMAZING POWER of things like this:
IF cardTotal(i%) <= 0 THEN card(i%) = 0
or perhaps using something like cardTotal(card(i%)).
A nice trick is to use arrays to make your output much simpler.
DIM CardNames(13) AS STRING
CardNames(1) = "Two"
CardNames(2) = "Three"
... etc. ...
and then you can PRINT CardNames(...something...) instead of having big SELECT CASEs. Same with suits. A similar idea can be applied to card values, although in blackjack aces would require special treatment.
Excellent work anyhow, and I'd love to see this program once you get it into shape.