Claire said it so well that I have little to add, but I'll add a bit about the word "will". The primary purpose of this modal verb is not to move action into the future. Rather, it is to express certainty, inevitability, or determination. (All of these are useful for moving action into the future, and that is why it is associated with "future tense".)
So, for example, you can say to your doctor "Every time I go into the swimming pool I will start itching". The word "will" is not needed in this sentence, but can be inserted to express the inevitability of this happening.
The sentences
"I go shopping tomorrow"
"I will go shopping tomorrow"
have the same meaning. The only difference is that "will" can add certainty, inevitability, or determination. This is especially true if you emphasize the word "will": "I **WILL** go shopping tomorrow".