We've installed the flooring and there is a half inch gap between the them. The flooring is installed on top of concrete. We have purchased a runner from home depot, however it did not come with any instructions and there are no pre-drilled holes. So how do we attach it? Glue? Finish nails into the laminate?

Assuming that by runner you mean some kind of wood edge molding. (to me a runner is a long narrow piece of carpet)
The best approach depends on some extent on how long it is l. If it is in a door way and about 3' long the best approach is probably to glue it down with construction adhesive. You will have to apply enough construction adhesive to the floor to insure that the molding is embedded in it. Weight it down for several days while the adhesive dries. Clean up construction adhesive with mineral spirits (paint thinner).
If the wood edging is longer than that you should probably attach it to the floor with fasteners. That will require you to drill holes in the floor and drive in wooden pegs, secured with adhesive. Then nail through the molding into the wooden pegs with finish nails. You can use screws but that would not be very aesthetically pleasing. Drilling in the concrete will require a hammer drill. Regular drill with masonry bits will not work.

Unlikely that trying to nail to the laminate flooring will work, its just not thick enough.