Intro
If building codes allow shallow footings and your deck requires only a few of them, you're in luck. You can probably dig the footings with a clamshell digger. In soft soil it's easy and inexpensive.
If you have a lot of deep footings to dig, however, rent a power auger. Rent a one-person machine if you have a way to get it home. Otherwise go for a two-person auger. In either case make sure the auger has a bit the right diameter for your footings. It should come with extensions so you can start close to the ground and dig to the proper depth.
Working a power auger can be a lot like working out at a gym. You and your assistant should plant your feet firmly and keep a tight grip on the machine. And when you lift the bit out of the hole, bend your legs and lift with them, not your back.
Don't try to dig through rocks. Remove the auger and try to pry the rock with a pry bar. If you hit bedrock, your code may allow you to pour concrete directly on top.
Prestart Checklist
Time
Figure about one hour for each 42-inch footing with a flared bottom
Tools
Clamshell digger or power auger, round-nose shovel, small sledge, handsaw, pry bar, 2-foot level
Skills
Digging or using a power auger, leveling
Prep
Remove sod, lay out site
Materials
Footing tube forms, mason's line