Adapted from another similar post:
1) You can watch tutorials for advanced techniques, for example these:
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part 1
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part 2
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part 3
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part 4
Concerning the basic stuff, as long as you understand all the moveset and you know how to recover (understand the second jump+Upb) you'll be fine. Oh and if you're not familiar with the terminology, you can read this
old thread. Some things might be outdated (like who says "ANA" nowadays?), but the basis is there.
Once you get passed that point, there are a few more things, some character specific, some general, like DI. Concerning the latter you can watch a
video I made. I'd recommend you forget about DI in the beginning though. And if you have questions about specific characters, ask in here if you don't find the info in other threads linked in the smash index.
2) You can practice on your own with training mode combos, but you'll never get so good by yourself. The best way to improve is to play online or to play against different good people offline. Playing CPU is not too recommended either, because things that work against real player don't work against them and things that work against CPU don't work against real player. Conclusion is you'll most likely only acquire bad habits. You can however practice some things such as combos/DI/z-cancel/other advanced techs, but don't try to win by every mean possible. Some good way to improve as a beginner is watching vids of pros and trying to do what they do (not too pro, because they'll often go for flashy stuff which is too hard to start off with).
3) Playing a lot of characters will help you have a better feel about the game's mechanics, however, if you're already familiar with the game, focusing on one char will help you improve faster in the beginning (doesn't mean playing only said char). That's my opinion, I know others may think otherwise.