how do you open the sim card slot on the phone?

If you purchased the phone without a SIM, it probably came with a SIM removal tool. If your phone didn't, a small paperclip, unbent should work as well. Insert the tool into the small hole in the SIM tray (on the right edge of the iPhone) and press firmly until the tray pops out.

How do you put the sim card in the little tray?

It will only fit one way.

Just lay it down in the cutout for it, matching the notch on one side of the card to the shape in the tray.

Its keyed so it will only fit correctly in the tray on way.