Pyrethrin, insecticidal soap, neem oil, spinosad and diatomaceous earth . These are the tools of *safe* insect genocide.
For spider mites, mix up fresh pyrethrin/insecticidal soap following the directions on the bottle. Some products like Safer's 3-in-1 come pre-mixed with Neem oil, which is cool but not strictly necessary at this stage.
For spider mites/thrips/aphids/fungus gnats/etc you want to do one thorough spray every 3-5 days. For spider mites i'd suggest every 3 days. These little bastards breed fairly fast, so you want to hit the adults before they lay eggs, the life cycle can be as short as 5 days from egg to mature egg laying adult, so 3 day intervals ensures you get the adults and you get the larvae/immature specimens before they can breed. Eggs can take anywhere from 3-8 days to hatch on average.
By thorough I mean you take your plant out, hit it from 360 degrees making sure that you hit the bottom of the leaves, stem junctions and new growth tops, look for creases and crevasses that look like they might be an attractive place for bugs to hide. I prefer to use my off-hand to brush the fan leaves upwards while spraying for the first pass or two, then hit the plant from the top down to ensure that it gets thoroughly soaked - I also give a brief spray to the top of the soil/coco to give any little bastards hiding there a bad day.
If your plant is small enough, dunking them is a really good idea.
If you can take your plants out of the tent/room for an hour or two, give it as deep a clean as you can stand. 20:1 mix of water to bleach (don't linger in the bleach fumes...), wipe everything down and then follow it up once dried with a brief spray of your insecticide. Repeat this every other time you spray.
I'd suggest repeating your spray or dunk 4-5 times at the 3 day intervals.
As an aside: For thrips you can be a touch more spaced out because their lifecycle is a bit longer, but you have to be sure to stay on top of your soil spray This is also where diatomaceous earth is useful, as it seriously fucks up the thrip nymphs, fungus gnats and any other bug that has a stage of life cycle in dirt. Dont' breath diatomaceous earth if you can at all help it (wear a dust mask), simply lay it down with fans off and walk away till it settles. I personally don't use the stuff, because i find pyrethrin and insecticidal soap to work well.
Moving on... once you think the little bastards are gone for good, spray one more time. Don't question it - just do it. There's no such thing as overkill with Spider Mites, only "Open Fire" and "Time to Reload"
From now on, your goal is preventative maintenance. Keep your room/tent clean, prune dying/yellowing leaves, ensure none stay on the floor. Every week until the 2nd/3rd week of flower spray with a neem oil or horticultural oil spray mix (rosemary/mint/etc blend).
Once you have completed your grow - dispose of your dirt and pots safely (compost/recycle) and repeat your deep clean - twice. Pay special attention to corners, around vents/mesh and the intake/output ducts. Do not use compost that has previously been contaminated with mites/bugs/molds unless you pasteurize it first and can be sure you hit 70*F for at least an hour.