Well, here's what I do...
There are a number of plastic "holding tanks" available in most pet stores... These tanks range anywhere from super-mini sized for under 5 bucks to jumbo sized at around 30 bucks.
I have a couple of these for several reasons. First of all, they make excellent "holding tanks" for when I need to quarantine a newcomer or when I'm cleaning out the main homestead.
They also make good transport vehicles because the lid snaps on and it's plastic and light.
When I bought my first pair of African Dwarf Frogs, it was on a roadtrip about a two hour drive from home. Given the long drive, I went ahead and bought a "Hagen Small Pal Pen" (mini plastic tank like the one pictured on the right), filled it halfway with water from their main aquarium tank in the petstore, and snapped the lid on with them inside. Then I had my friend hold them on the trip home. (The water was filled halfway so we wouldn't get frog-water all over my car and all over my friends' lap.)
For my firebellies, I use a slightly larger tank of the same style. I usually put about an inch of water in, plus I drop a plastic plant in so they have something to climb onto. Remember, you don't want to stick anything heavy in the tank like large rocks or decorations because if the car shifts you might end up squashing your poor frog quite flat!
Below are some listings where you can see prices and pictures, but these types of plastic tanks, or ones similar to them, can usually be found at any neighborhood petstore.