I have 2 pieces of stainless steel 16 gauge that I am putting on a countertop. How do I join them together? Do I just butt them together and caulk? Or is there some other way?

I would either use epoxy cement or solvent based contact cement. If you use epoxy, mix it and spread a thin coat. Place the two together and set bricks or weights on the sandwich. I'd use 20 minute epoxy. If you use contact cement, spread a thin coat on each piece, let them dry so they aren't tacky, separate the sheets with newspaper or brown paper, align the sheets and slowly slide the paper out while pressing on the remaining stainless. Use a rolling pin to press the sheets together. I've done both but prefer the epoxy.

Think I misread the question. I was referring to laminating 2 sheets together. I've done that with 24 gauge. I assume you are just laying the sheets on the counter and butting the sheets. First, you need to adhere them to the top. Use the above ideas or use a mastic. Then, silicone a small line down the groove.