Originally Posted by MRT2

If you got the hang of shifting with your old 10 speed, you should be able to shift your current bike. First of all, it isn't a 21 speed, it is a 3 x 7. 3 chainrings up front, and 7 cogs in back, which is only 2 cogs more than your old 10 speed, which was a 2 x 5. Now, the small chainring is likely a very small gear, so for now, forget about that one and focus on the other two chainrings. Start out using the middle chainring and leave it there until you get the hang of things. Now, when you start pedaling, shift into a gear that allows your legs to spin the pedals at about 80 to 90 rpm and still feel some pressure. If you are pedaling like crazy and not feeling any tension, than shift to a harder gear. If the pressure is so great your legs are getting gassed or you cannot maintain at least 80 rpm, shift to an easier gear. That is it.

As for the tires, those knobbies are poorly suited for paved surfaces, so if you keep this bike, you need to budget $40 to $70 for some new tires. That free bike is not free and not worth putting any money into. an expensive lesson, but maybe it is time to consider cutting your losses and starting over.