Ah, the highlight of Half Life 2. The weapon that makes this deathmatch oh so different. Well, here I will talk about beginner moves with the gravity gun. Ill leave the harder things for later.
How powerful is the gravity gun? Very. As long as there is any object, from a rock to an entire car, you can damn well kick ass with it.
Punting/Picking: So obviously, we can see the primary attack function of a GG. Now different objects can serve many purposes. For Example, if you picked up one of those long steel tables, you could hold it in front of you as a shield against bullets, (although you are still vulnerable on your legs or whatever its not covering). Keep in mind although larger objects are larger shields, you lessen your field of view. In close quarters combat, if you miss with the GG, immediately pick up whatever object is closest (because this is fastest) and launch it right back. Sometimes that closest object is the very one you fired off a moment ago, but bounced off a wall.
Keep in mind two things. One is that some objects are weaker than others. A breakable crate wouldn't hurt as much as a steel barrel, (although usually you would probably own them anyways with a direct hit) and second is that some items are hazardous to your health. I'm talking about Explosive Barrels in particular. Hold it too long, someone is going to shoot it and you will blow up.
Large objects likes cars can be used to frag, but only by punting (primary fire). Your target has to be on the other side, and you have to keep punting it forward till it squishes him :]
Grenade Launcher: Remember you have a key binded to GG. Switch to grenades. Throw grenades. IMMEDIATELY switch to GG and pull on the nade while its barely left you. If done fast enough and correctly, your GG will be holding a live grenade. Now obviously you have like 2 or 3 seconds before your face explodes, so launch it fast. This is rather hard to do, but if you manage to master it, you can have a virtual rocket launcher every time you spawn! O_O
Out of Reach: Remember that rocket launcher in the vents in dm_lockdown? Where if you went in, some asshole on the other side turns on the fan and you die? Or that time you might have survived if you had reached the item stash in another second? Your gravity gun might just be the answer. You can pull weapons/health/batteries from dangerous places. Just don't launch the weapons/medkits at your enemy, because it just buffs them.
Catching/Returning: Damn that GG whore! Keeps pummeling you with boxes and barrels eh? Well give him a taste of his own medicine! Keep your finger holding on the secondary fire while pointed at the target. He will launch something at you, and 75% of the time your GG will activate at the right moment, catching his gift to you. Immediately thank him by launching it back. If you are really fast with the clicking, he could be dead before he takes another step.
This also includes grenades tossed by other insolent fools, which you can receive and donate right back (remember the timer though. Too long and its not worth picking up.)
Most interesting of all is the combine energy ball. You know what I'm talking about. That secondary fire on the Combine Pulse Rifle. Such a powerful weapon... Someone thinks hes got you? You hear that energizing sound? See that ball coming at you or bouncing around the room? Grab it with the GG! Then launch it back at him, or release it in the room. The moment you grab it, the ball "changes sides" and will no longer harm you, but your enemies. Keep in mind that your enemies can do likewise.
So that's the beginners tut for using the GG. I may or may not make a higher level tut for using the gravity gun, or add onto this. There are other skills possible such as high jumps with the GG. Unfortunately this is the beginners tut, so only simpler common stuff is in here. You will probably witness this guide in use when you play next time.
Good luck and happy fraggin!