Hey, welcome to the world of reptile keeping!
I have never kept a reptile, and I don't really know where to start (habitat wise). My tank is only 12 inches (30.5 cm) high. Is this tall enough? I want to start out with two anoles (females) and I don't know if this will provide adequate climbing area. I also don't know if this will "cook" the reptile I choose, if the light is to close.
Unfortunately, a 20 gallon tank is definitely not big enough for anoles. Although they are small lizards, they are very active! I'm struggling offhand to think of any lizard that will comfortabley fit in a 20 gallon tank as an adult, short of pygmy chameleons. 12" is very very low and personally I think your tank may be far more suitable for an invertebrate or amphibian. This tank may be suitable for a juvenile, nocturnal animal such as a baby leopard gecko - but you'll need to upgrade as they grow.
I am also in the dark (pun intended) about lighting. I have looked around and I don't know what watt bulb I need. I also don't know if I need a timer for the lights, or if I can change them manually. Do I need two lamps, or can I change the bulbs back and forth?
If you did decide to go for an anole, or any other diurnal (daytime) lizard, you would need two types of lighting - one, a UVB light (usually in the form of a tube). This is usually 8 or 10% depending on the species. This looks like the type of bulb you get in fish tanks, but those are UVA, so you need to make sure it's specially a UVB one for reptiles. Without it, the majority of diurnal lizards will not be able to correctly metabolise the calcium in their food and will get a disease called Metabolic Bone Disorder, which eventually is fatal.
The second light you need for a daytime species is a basking bulb, providing a localised high heat output.
Nocturnal animals such as leopard geckos, crested geckos, snakes, and also invertebrates and amphibians do not need any lighting so if you're not looking to invest in a lighting setup, I'd be looking in that direction.
I think the rest of your questions may be better answered when you finalised the species you're going to keep and then people can give you a better idea
One thing I will say is that you may find, although your friend has given you this 20 gallon tank for free, the expense of setting up a reptile enclosure is often not the tank itself, but ensuring that the environment is correct in regards to heating and lighting and then adding safety equipment such as light guards, thermostats, thermometers, humidity dials and then the decor itself. You may find that your local reptile shop does a complete setup that actually saves you a lot of money - or you can usually find second hand setups - often with the animal - locally.
I'd recommend deciding what species is best for you - afterall, most reptiles live 10, 20, some even upwards of 30+ years, so deciding on the right pet for you and then creating the right enclosure may be better than trying to find something to fit into this tank you've been given.