I'm expecting some new strings in the mail within the next few days. They're D'Addarios ; .011 - .049. I'm not sure what I have on it now, but they are the strings that came with my Epiphone SG G400 from Musician's Friend. They're definitely thinner than what I've ordered. So do I need to adjust my bridge or anything to avoid damage to my guitar? Is it a hard process?

I assume UG will tell me how to do a new set-up. I'd rather avoid doing a set-up unless I have to.
You might want to adjust the action and intonation a bit. You'll probably need to adjust the truss rod if it's a big change in tension too.
Got on the bus with me daysavaaaa
If your action is already quite low, you might need an action change to avoid buzz. Aside from that, just put them on and wait a little while and see if your neck relief changes at all - if it does, then you'll need a truss rod adjustment; otherwise, you're set.
Ibanez RGA121 | ESP LTD H-1000
Axe-FX Standard
the epiphone g-400 comes with 0.10 gauge. so you probably don't need to get a set-up
A hero of war, Yeah that's what I'll be

So if anything, I'll just have to adjust the truss-rod? What kind of tools do I need for that? This is the firs time I'm trying it on my own. I'm at college so I'm not sure I'll have what I need. I don't want to break anything...