[1crosscut]

The oil pump is held up into place by a fairly large spring on the bottom of the oil pump pressing against the bottom of the oil pan.

When you remove the pan the oil pump is free to drop away from the engine. Sometimes is stays in place just waiting for you to move your head underneath of it and then it will fall out at that very moment.
Just reach in and give it a tug straight down as you lower the oil pan.
Rebuild kits are available for oil pumps if you want to go that route instead of purchasing a new one.
There is a small threaded opening on the right side of the block with a plug in it.
You can remove that plug and use a special threaded insert and bolt that screws in there and will hold the pump in place. Not necessary for removing the oil pump but very handy for installing it. It is a tapered pipe threaded fitting so do not use a bolt in that hole. It will damage things.
Les Andrews Mechanics Volume One Mechanics Hand Book has very good instructions on doing this.