The main type of fu'ivla that you should make on the fly or as a beginner is a type-3, and the rules for making those are quite simple: start with a consonant, end with a vowel, and choose a gismu to stick on the front with an -r- like "brodr-". Besides being easy to construct as far as the word-construction rules, such fu'ivla are also easier to understand, since you have a clue what category of thing you're talking about.
One of my favorite works in Lojban is "la grutrduriani" (Durian fruit), by Viktor Medrano. http://www.lojban.org/tiki/tiki-download_wiki_attachment.php?attId=594&page=Viktor%20Medrano It's the first book I was able to read and enjoy without constant trips to the dictionary, and part of what makes it so comprehensible is heavy use of type-3 fu'ivla: kelcrfudboli, kelcrfrizbi, grutrduriani, bangrnuktituti, vrusrpandanu, cidjrlomeini.. to the untrained eye those look like monsterous words, I suppose!, but if you recognize a fu'ivla when you see one then you can piece them apart. :)
Shorter form fu'ivla are only for those fu'ivla which are the most common and established and ordinary, so as a beginner you don't have to worry about how they're constructed. Just learn the few fu'ivla that you encounter-- I like "djirafa", giraffe, "odbenu", walrus, "spitaki", parrot, and "alzaitu", olive-- and if you feel like inventing your own fu'ivla, make a type-3. If you make a fu'ivla that's so popular it should be shortened, we'll help you figure out a short form that works.
mu'o mi'e se ckiku