Tatacoa desert is situated in the northern part of the Huila region in Colombia – the closest city is Neiva, with the picturesque town of Villavieja an hour from the desert itself. It's very hot, so if you go remember to pack shorts and plenty of sunscreen!
Our bus from Armenia cost 40,000 COP each and only took 7 hours because the minibus driver was a maniac. There are a ton of companies that travel there, so check them all out and don't be afraid to try and get a discount (we did, because we booked four tickets at once). There are fairly regular truck-taxis going from the Neiva bus station to Villavieja and then on to Tatacoa, and it costs 15, 000 COP for a one-way trip (which lasts an hour).
Tatacoa is basically a road, with a few hostels along it. Villavieja is the closest place for actual shops, and there are nice hotels there, but they're more expensive than the places in Tatacoa. We stayed in a hostel called Sol de Verano for two nights, which has rooms available for 20,000 COP a night (which is VERY cheap), although they charge for meals (breakfast was around 6,000 COP and lunch/dinner were something like 10-12,000 COP each, but the food was really nice).
Our room slept four (two single beds and a king bed), had a working fan at night (it was stifling in the room, despite it not been entirely closed-off from the outside world) and the toilets and showers (with cold water) were outside (but private).
The desert has a few different areas to walk around, though we stuck to the 'red' part and easily killed a couple of hours during the morning then another couple of hours in the evening. There's a ton of bird life in Tatacoa and, if you're lucky like us, you'll get to eyeball some lizards too.
The return journey cost another 15,000 COP each, with another group discount of 40,000 COP each to get back to Armenia (which took a bit longer, but mainly because it was a proper coach and we stopped at a pandera (sort of like a service station, but not fancy at all) for maybe 30 minutes so everyone could stretch their legs and get a bite to eat.
So, looking at transport and hostel costs only, you'd be spending around 150,000 COP (with meals extra). We also spent a night in Neiva itself, but I wouldn't recommend that, mainly because the city is really hot and there's bugger-all to do there, other than check out a few okay bars and a blindingly-lit pool hall.
Oh! And one last thing, that was impossible to capture in the video or in photographs: the night sky in Tatacoa is incredible for star-gazing. There's an observatory there that charges, I think, 10,000 COP, but we just sat out in the hostel car park after 10pm (when all the lights were turned off to save electricity) and got to marvel at one of the most beautiful sights on the planet – you can even see the hazy glow of galaxies! I tell you, it's astounding, and if you only go to Tatacoa for one thing, go for that.