I have been housesitting for some folks for a few months. They have a juniper bonsai that they told me to "water about once a week with a trickle for about 5 minutes."

I decided to do my own research and that didn't sound right. When I emailed them they said "Just make sure the soil is kept damp." They keep it inside by a window.

Everything I've read seems to say to keep it outside. I live in Texas where it's been super hot (and is for 8 months of the year). It's just now starting to cool off a bit. Anyway, I wanted to post a picture and see if any of you could help! I don't want to kill the tree!

Hello...
Hmm, sorry, but it looks dead already, simply because it was indoors...
Does this pot has a drainage hole? I mean, it wouldn't save it from death from indoors, but not having it can make it quicker.

About your climate, I don't know about the best species, but I'm sure there are some types of junipers growing on Texas fields, right?

It does indeed have a drainage hole. That is unfortunate!

Yep, it is unfortunate, Junipers indoors tend to die on a "silent" way, because they still green when dying or dead for sometime, when it goes brown, it means it's been dead for a while...