My first question is what the footing will carry, a full wall or a single pier or column, because that decides the type of footing before anything else. Then I look at where your water runs and what the ground is like, and we have underground lines marked before anyone picks up a shovel. Our crew digs the trench or holes, sets forms where the ground needs them and ties in rebar, the steel that keeps the concrete from pulling apart, and if a trench goes too deep, we fix it properly instead of shoveling loose dirt back in. After any inspection the job needs, we pour, finish the top and let it cure, the wait while concrete gains strength, before anything gets built on it or dirt goes back. Nobody sees the digging once the wall is up, so it's the first place people want to save money, and it's the one place I won't, because a footing on bad ground lets everything above it move too.
Footings often come with other work. When an old slab or wall is in the way, or you need an opening cut in existing concrete, concrete cutting clears the spot cleanly first. If something you already have has settled because its footing let go, foundation raising may be the job instead, and I'll tell you on site which one you're looking at.
Continuous footings for walls
A continuous footing runs the whole length of a wall or foundation, so it suits block walls, retaining walls and the edges of an addition, anything heavy that sits along a line. The wall gets a wider base than itself to stand on.
Pad footings for posts, piers and columns
A pad footing is a single block of concrete under one concentrated load, like a post, pier or column. It suits patio covers, decks and porches, where the weight comes down in a few spots instead of along a line.