How can I fasten a threshold to concrete?
There are two recommended approaches:


Use plastic plug anchors. Use a hammerdrill or rotary hammer to drill holes sized for the plugs--typicaly in the 5/16" to 3/8" range. Drive the plugs in with a hammer and run the screws into them.
The advantage of this approach is that you can use a variety of screw types, depending on your needs, as long as they're the right size for the plug. Also, the plug can be removed and replaced if necessary. A disadvantage is the larger required hole size. 

Use masonry screws. Pilot holes using a hammerdrill or rotary hammer according to the manufacturer's specifications. Drive the screws directly into the concrete. 
The advantages of this approach are the smaller hole and greater holding power. Disadvantages include difficulty in driving the screws, the chance that the screw strips the concrete, the non-reusable nature of the system, and the limited head styles. 


With both approaches, precise hole placement is critical. There's virtually no adjustment in position once they're drilled.