First of all, I carry a firesteel as a backup to a mini Bic or matches and I also carry a spy capsule jammed full of Tinder Quick tabs. Other fire starting backups are an Esbit tab and my alcohol gel hand cleaner. You can pull lint from your socks, hat or fleece, or even use some polyester fill in an emergency.
In use, I put the end of the firesteel right down on the tinder and strike down to it. I normally use a knife rather than the scrapers sold with the steels. A broken off hacksaw blade makes a good scraper too. My survival lanyard has a Victorinox Classic and a firesteel along with the spy capsule (along with a micro LED, whistle and compass). The larger steels are are easier to hang onto and last longer, but you can still get a good steam of sparks off the smaller ones. They do work better once you get through the coating and a flat develops. I find most people try to scrape really fast, which isn't necessary– a slower stroke can produce more sparks.
Tinder needs to be as dry as possible. Carrying dry tinder is a smart thing to do. I have used Tinder Quick tabs as a backup as they are prepared and can be very compact. Dryer lint works and is about as cheap and easy as it gets. You can jam some in a small bottle for safekeeping– I have used prescription pill bottles. Vaselined cotton balls work very well and burn long enough to give you all kinds of time to pile on smaller sticks and shavings. Likewise Esbit tabs, which burn really hot. For a real lazy method, put a dab of alcohol get hand cleaner on a fuel tab and give it a strike with the firesteel– it will take right off. Don't completely depend on such methods as you might not have them available when you really need them.
Others listed natural tinder sources. Finding sticks and shaving them down to drier inner wood is what I usually end up doing. The outer parts of dead wood may be wet, but the inner parts can be dry. You can shave a stick down with a smaller knife, or you can baton a larger knife through a piece of wood to get it down to kindling size and the drier inner wood. Learning to make fuzz sticks is a part of bushcraft and is a time honored way to teach knife and fire starting skills– it's a Boy Scout thang for sure.
Fatwood is another natural tinder source. You can carry some with you or you may get lucky and find a fatwood stump in your travels. Fatwood is typically a pine stump where the resins have collected. You can buy commercially packaged versions.