BMitch is overall correct. If you cannot afford to fix it right now, you can buy time by applying a hydrophobic grout sealer. This will not stop water, but will cut it back substantially. You will have to periodically renew it. I would use one that soaks in, as opposed to a surface layer. Usually it will take several applications to get to the point where no further soaks in.
You can also buy time by keeping the bathroom dry. Run the fan! Run it for at least an hour after anyone has steamed up the mirrors.
It also will help if the spaces where the water is getting to can be vented.
And of course, decreasing the frequency and length of use will help. (half shut the hot water line to this shower. Cool showers tend to be short. If they cut the cold to get it warm enough, then water isn't hitting the walls very hard.
But you need to fix it in the long run. The above can postpone it a few months to a few years, depending on to what degree you apply them.
The usual standard now requires cement backing board, what amounts to a waterproof coating, or a layer of plastic (Ditra system and similar) then your tile.
Last winter I ripped out the free standing ugly plastic shower stall and did my own. The prep work was FAR longer than the tiling. I did cheat and used a pre-formed fiberglass base.
As far as I can tell showers are a "Do it right, or do it over" It's really hard to fix it. (I now, however, always leave an access panel to my plumbing so I can replace taps 20 years from now, and check for leaks. )