You must follow all normal timing rules when casting a spell with web-slinging. For creatures, that usually means you must cast it during a main phase of your turn while the stack is empty.

Web-slinging represents an alternative cost. If another effect allows you to play a card for a different alternative cost, including "without paying its mana cost," you can't also choose to pay its web-slinging cost. If any additional costs from other sources are applied, you must pay those.

If any permanent has an ability that triggers when the permanent you return leaves the battlefield, that ability will be put on the stack after you finish casting the spell, and it will resolve before that spell.

The creature you return must be tapped at the time you pay costs, but doesn't necessarily need to be tapped before you start casting the spell. For example, if you tap a creature with a mana ability to pay part of the spell's web-slinging cost, you could also return that creature to your hand to pay the cost.