We installed new hardwood flooring on our slab floor, it is a floating floor. How do we transition to tile and carpet? Do we need to glue the transitions down?

Since this is a floating floor I will assume it's a laminate, right? All laminate floor companies make their own transition piece. If you know the brand name then just Google something like Armstrong laminate floor transition and you should see what you need to buy and they do get attached to the floor but usually with drilling and plastic inserts with screws.