Use set when someone places something somewhere. Use sit when someone takes a seat or when someone or something rests in place.
Check whether someone is placing something
- Set. Jules set the mug on the side table. The mug is the thing Jules placed, so the mug is the direct object.
- Sit. Jules sat in the armchair. Jules took a seat. A thing can also sit somewhere, as in The mug sits on the side table.
Use the right past form
The past tense and past participle of set are both set. The -ing form is setting. For sit, both past forms are sat, and the -ing form is sitting.
Other senses have their own patterns. The sun sets means it goes below the horizon. Jules sat the child on the bench means Jules seated the child. Compare Lay vs. Lie for a similar placement and position distinction.
