You can make refrigerator pickled products that must be stored in the "refrigerator" and not in the cupboard and you can Boiling Water Bath pickles that can sit in the cupborad until you are ready to open the jar.
Type the following words into your SEARCH engine box: Colorado State University Extension and pickling.
You will get some great recipes. You could also get a copy of the Ball Blue Book at any grocery store,k hardware store, or bookstore. It has some great visuals to help you with your canning and pickling.
Enjoy and if you still have questions please call me at the CSU Extension of Boulder County office at 303-678-6238

Do you mean Persian cucumbers? You can quick-pickle them in a solution of water, distilled white vinegar, salt, sugar and minced fresh dill. Slice them crosswise. Stir together the brine, taste for a good balance of sweet and salt. Add a few whole peppercorns if desired, stir in the sliced cukes, top with thinly sliced white or pink onions and marinate a few hours or overnight. Don't know about beets, I haven't pickled them.

Here's a basic recipe I use; cook the beets before pickling!

1 cup white wine vinegar
1 1/2 teaspoons sea salt
1/2 cup sugar
1 cup water
Boil the ingredients together for a few minutes until blended; pour over the beets and refrigerate five days or so.

Making "real" pickles is somewhat more complex and they are best refrigerated rather than shelved. Creamtea's recipe is perfect for quick pickles!

I'd like to pick pickles - preferably the little Persian ones. And red beets.

What is it that you wish to pickle?