There are only a few things to know that can insure your ukulele will last a long time and continue to sound and play well. Laminated instruments take a bit of care, but solid wood instruments require more concern, even under "normal circumstances". First lets go over things that all ukuleles require:
1. Normal temperatures. So no hot or cold cars for much more than you would like to experience. Cracking/warping/glues loosening etc. can occur.
2. New strings at least once a year. Twice a year or more if you can. Even if they don't break they get inconsistencies in the radius. Intonation, or the accuracy of the pitch as you go up the fretboard, will usually go off on at least one of the strings. It is not always a visible dent in the string, but there is a precision with a rectified new string that gives a clearer more accurate tone.(koolau,aquila...). Be aware that strings stretch out so you may go out of tune for a while, this also depends on how much you stretch them out. Here's a full How To Video/Tutorial on How To Change Ukulele Strings
3. Ukulele Cleaners (optional): Do not use furniture polish or just any wax on your ukulele. It may not be a problem, but it can be. If you don't want to buy another cleaner just for your ukulele, then use a very lightly dampened rag wrung out and wipe dry. A common favorite for cleaning minor stuff is the Dunlop 65 guitar polish and a micro fiber cloth. If you want to find something at wal-mart or maybe your hardware store that will really gloss up your finish try the Turtle Wax Premium Grade Rubbing Compound (says clear-coat safe). This will be fine on any gloss Asian import but I would not use it on a higher end uke or Hawaiian maker. There are a number of guitar polishes you can use.
Ok, so what about Solid wood instruments? What else do they need?
The main thing to do with a solid wood instrument is have a humidity gauge where you keep your ukulele and if you are below 35% or above 65% humidity, have a means of humidifying or dehumidifying. If you buy a solid wood instrument from The Ukulele Site YOU ALWAYS GET A HUMIDIFIER FREE!!
Humidifying - The most common problem is your humidity levels being low. This is often bad during the winter or summer months when there is a lot of air heating/cooling. Or in states like California/Arizona/Nevada etc..where it is very dry. This is also the biggest problem your instrument can encounter because it quickly leads to neck angles being off, fret ends are often sticking out, and in extreme cases cracking occurs. So what you do to prevent that is, when you are not playing it, keep your ukulele in it's case with a humidifier. The Herco HE-360 is what we commonly give with all solid wood instruments. Also, the Oasis Ukulele Humidifier is even more effective in extreme changes. But one major thing that should be noted is that you need to maintain your humidifier. Follow the directions. Just having it is not enough.
So what about us humidified people? Very humid environments can cause an ukulele to swell and get higher action or get a "tongue rise" causing buzzing. If you can, have a room with an air conditioner or dehumidifier to keep your instruments. More than likely you don't, so you can get the Planet Waves Humidipak. It is not inexpensive, $40 but may be crucial for continuous optimal playability.
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