Hi there.

I'm confused about something, when it comes to changing strings on my electric guitar.
If I get a guitar, for example a new one or just one I bought second hand, and that guitar is used to have a speciel string guage on? Will it then be a big deal to just change the string to the gauge I like? I mean, will it mess up the guitar? For example when it comes to intonation and setting the guitar up correctly?
I like 10's..

There's nothing special about gauges, use whatever you want. That said intonation can be changed, and you may also want to look up how to adjust the truss rod.
RG351DX - Bridge Dragonfire Screamer, Mid+Neck Fender Hot Noiseless
Peavey Valveking 112 - Eminence GB128
AMT E1 > Joyo AC Tone > Dan'o EQ > Shimverb > Digidelay
Strings are cheap. Try a set of tens and check your intonation. It's not difficult to adjust if needed but I use different gauges for different projects and intonation is always pretty close.
"Your sound is in your hands as much as anything. It's the way you pick, and the way you hold the guitar, more than it is the amp or the guitar you use." -- Stevie Ray Vaughan

"Anybody can play. The note is only 20 percent. The attitude of the motherfucker who plays it is 80 percent." -- Miles Davis

Guthrie on tone: https://www.youtube.com/watch?v=zmohdG9lLqY
Not to unnecessarily confuse but changing string gauges may require more than just an intonation tweak. A gauge change may cause the neck to shift slightly in response to the different string tension. Likewise, if your guitar has a tremolo style bridge you will probably need to make some adjustments there to compensate.
Charvel DX-1 FR / DS-1 ST / DC-1 FR / Custom Strat / La Patrie Hybrid CW / Vypyr 30 / VK100 / 1960A