I have never raised a house plant before. I know virtually nothing of plant biology, except that they need soil, water, and sunlight. The thread title is a little misleading, as I haven’t even killed enough plants to have learned from that experience.
I want to raise a plant that is very difficult to cultivate in my home: a lime tree. I think I have read enough to determine that this task is not completely impossible, but I’m certain I will fail at my current level of knowledge and experience.
How do I get from where I am now, to where I want to be?
What books do I read? What should I use as my practice plants?
For a lime tree to actually flower and fruit indoors you will most likely need supplemental grow lights. At a minimum you would want to have a sunny southern exposure window for it to sit next to. Better yet would be to be able to place it in a sunny location outdoors during the summer months and only bring it inside during cold weather.
A good rule of thumb for most plants is that it is better to under-water than over-water. Overwatering causes root rot which is hard to recover from. Underwatering can be corrected much more easily if you are paying attention to the plant (most plants will recover if you water them right away when they start to look droopy, though of course there comes a point of no recovery from that too if you are neglecting it).
I think gardenweb is a great resource for advice and information on plants. The citrus forum would probably be useful: http://forums.gardenweb.com/forums/citrus/
If you have a good sunny window space it would be reasonable to try potted citrus, if you research its requirements beforehand. To get both flowers and fruit, your best bet would be either a Ponderosa lemon tree (very large fruit on a small plant) or a calamondin orange tree, which flowers and fruits heavily when happy.
You’re right though that it’d be a good idea to work up to the citrus by seeing how you do with easier houseplants. Examples are Chinese evergreen (which has a cool white spathe flower) and variegated Scindapsus aureus. Both tolerate relatively low light (a bright window without much direct sun is fine) and a degree of neglect. Get a lightweight potting soil mix to use indoors and learn the first rule of watering, which is: water when the upper soil levels in the pot have started turning dry - not a set watering schedule which is a recipe for overwatering (usually) or underwatering.
Best of luck.