I would guess you can just take a private taxi.
If you're on a budget, I can offer the following information.
I didn't fly into Maseru. I took a minibus to Maseru, then another minibus the next day to Semonkong Lodge (I highly recommend Semonkong Lodge).
When I returned from Semonkong to Maseru, I wanted to go straight to the airport. I got a minibus from Semonkong to Maseru and asked them to drop me near the airport. They dropped me off at the gas station/junction about 6 kms from the airport. If you look at google maps, the gas station is at the junction of Main South 1 Road and the road to Roma/Semonkong.
From the gas station, I stood on the road towards the airport and shouted "airport" whenever a minibus came by. After 4-5 tries, I caught a minibus going to the airport. The minibus actually served a local route, picking up and dropping off passengers who live in the villages along the airport road. It went down Main South 1 road and then turned left and then right onto the smaller access road that runs right pass the airport entrance. They dropped me off just outside the airport gates.
So if you're on a budget, you can probably walk from the airport to the road, flag down a minibus for pennies heading up to the gas station, then get another cheap minibus into Maseru. OR they may have minibuses directly from the airport into Maseru.
It's all very safe (daytime, anyway) with no ripoffs or hassles.