If you are coming out of the airport parking lot, after you insert your token to get out, you will turn right. There is a new temporary roundabout at the south end of the airport. You will use this and then head back toward downtown.
When coming back to the airport, the airport entrance is now (temporarily) a veer toward the right on a frontage road before you get to the airport. Part of this new temporary road is one-way and part is two-way. Just keep your eyes peeled.
Even a trek going past the airport (we went to Savaneta 3 times during our stay) is a little tricky. Again, just be alert.