I recently built a garage and have a question. I have 200 amp service in my house. I ran 100 amp triplex in 2" conduit out to my 100 amp box in my garage. I don't have any extra lugs in my 200 amp panel in my basement or in my meter panel outside. What would you recommend I do to power up my garage?

Change out 4 of your regular breakers for 2 "slim line, 2-in-one, piggy back" breakers (what ever they are called for your brand of panel). That should free up 2 spaces for a 100 amp breaker.

I have 10 vacant slots left in a new Square D panel in my basement. So I can use a 100 amp breaker right out of my panel using the triplex I ran out to the garage? Thank you for the response.

Triplex? You need 4 wires to that garage panel. So you already have a sub-panel in the basement? You can feed the garage with that. Keep in mind that only the main panel can have the neutral and grounds on the same buss. All subs must have 4 wires going to them, with the neutral and the ground buss separated, and the neutral not bonded to ground.

I have a square d 200 amp main in my basement. I now have a new square d 100 amp main in my garage. I also have 2" conduit underground with 100amp triplex installed because of advise from another source. So here I am, trying to figure out how to get it powered up. (after inspection of course) I could have gone with a sub instead of a main out in the garage if I come out of my 200 amp main in the basement, right? Or did I get that wrong? I just want to get everything in place and right so it will pass inspection.

Your garage panel, if powered from your main panel, is considered a sub. I'll assume it's not an attached garage. So what you will need from the main to the sub is 4 wires... 2 hots, one neutral and one ground. What you will also need at the garage in an additional ground rod with a grounding wire to the sub panel. Whom ever advised you to run 3 wires and not 4 was mistaken.