Learn Hardcore Greek: Στο πλυντήριο βάζω απορρυπαντικό και μαλακτικό, αλλά όχι πολύ. - In the washing machine I put detergent and fabric softener, but not a lot.

Στο is a contraction of σε + το (in/into + the).
So Στο πλυντήριο literally means in/into the washing machine (or sometimes at the laundry/washer, depending on context). Greek commonly contracts:

σε + το → στο
σε + τη(ν) → στη(ν)
σε + τα → στα

Why is it πλυντήριο and not something like πλύσιμο?

πλυντήριο is the common word for washing machine. It can also refer to a laundry place in some contexts, but in a household sentence like this it almost always means the machine.
πλύσιμο means washing as an activity/process (e.g., Το πλύσιμο των ρούχων = washing clothes), not the machine.

What does βάζω literally mean here, and is it the normal verb to use?

βάζω literally means to put / to place, and it’s very natural in Greek for “adding” things to a machine or container.
In this context it corresponds to I put/add detergent and fabric softener.

Why is βάζω in the present tense? Is it “right now” or “in general”?