guard basically revolves around how ur hav ur opponant in your control wen they are on top.if they are between ur legs (kinda in the sex missionary position :P ), thats full guard. bhasically from here you can control there movement better, an launch ur own submission attacks ect, or jus clinch for dear life until ref stands u up lol.
half guard is where u have 1 of their legs between yours, which means they have more room for manouver, but i find its easier to sweep them an get back to feet(or get on top of them). after this theres side control (where they lie on ur sideways, so ur chest to chest in a T shape), an full mount, where they have their legs over ur waist so basically they r sittin on your stomach or chest.this is the worst place to be as you dont have many options on how to escape or block the ground an pound!
these are very bacic descriptions, an there are loads of variations, but you need to see them in action to understand them. my advice is to jus watch as much ufc/MMA or wotever as possible, an just listen to the commentary an how they describe the action. joe rogan who commentates ont he ufc events usually breaks down the moves an transitions pretty well,watch a load of old ufc events on youtube or download em off utorrents ect, an yall quickly work it out.
failing that, the logical answer wud be to just ask your gym tutor to show you you quickly at your next session