Taking care of your guitar is important because these instruments are your investments and for a touring musician need to be in peak condition to prevent things
Keep it Clean
The best way to take care of you guitar is to keep it clean. Harsh chemicals from the oils in your skin can cause the dyes and stains in your guitar to discolor or eventually flake. Every guitarist should own a microfiber cleaning cloth and guitar cleaning fluid. Using anything else can scratch or damage the finish.
Watch the Strings
The worst thing that can happen to a guitarist is to have a string break in the middle of a performance. Sometimes this can't be avoided but if your strings are starting to show signs of wear, like becoming dull and brittle, then its time to change them out.. Its better to have fresh (and tuned) strings than risking a break on stage.
Don't lean the guitar
When ever possible use a proper guitar stand to keep your guitar sitting up. Leaning your guitar neck or head agenced an object like a table or amplifier can bow the neck. Cuaseing all kinds of problems with intonation and playability. This isn't something that can happen overnight but over time the neck can and will bend.