You can familiarize yourself with many components, parts etc, by looking at catalogs and manufacturers' websites of same items.
Another clue to look for on circuit boards, are the component designation legends sometimes screenprinted onto the boards before they're stuffed/populated with te components. Fuses, for example, are generally designated Fx (F101, F200 etc). The components on that particular board may, or may not, be clearly marked.. but as you take more stuff apart (and it sounds like you will be), you'll become more familiar with various components' appearances. Eventually, you'll be able to spot items as scarce as SMT fuses very quickly, at a glance.
That's how it gets started. Before ya know it, you'll have piles of stuff sitting around to tear apart. It's not like there is likely to be a shortage of inoperative electronic gear, any time soon.
Alternatively, research websites for similar problems with the same brand/model of laptop. Having a little too much knowledge never hurt anyone that I know of.
Save shortcuts to helpful websites and make some notes (paper or text files) for future use.
Generally, open fuses aren't the only problem, but with a charging circuit, it's possible that a weak or defective/worn out battery may have caused the fuse to open. Checking other components in the vicinity with an ohmeter may reveal other stressed or faulty components. Many modern components don't show visible signs of being defective, so a decent DMM digital multimeter will prove to be very useful in doing quick checks of various components. Working on and testing low voltage circuits is generally fairly safe, but be sure to read and understand the cautions regarding safe use of testing equipment and use the precautionary info to develop safe work practices.
Over the years I've heard/read that there are some good DVDs covering a lot of topics related to basic electronic circuits, so some of those may be beneficial.
-- Cheers, WB .............
This is where I have to admit to a considerable amount of ignorance. What would a surface mounted fuse look like and would it be visibly blown?
Tim (apologies for stupid quoting. Using my wife's Vista disabled laptop).