Unless you're trying to get a big ticket item cheap or whatever, you don't need any complicated systems, at least I've never had to use much. You just specify the item, or the links/stats you want if it's a rare, you can set a maximum price(it convert currencies to chaos equivalent value based on their currency exchange rates, so even if you set it at 1chaos, you'll see stuff for alts/alch too for example). It's all very self explanatory. Once you've done a search, you can sort by clicking on one of the boxes to sort by that, for example by default it sorts by price, from lowest to highest, but if you click on quality, it'll sort by quality instead. Clicking on currency again will revert. You can also then do a live search, which is basically the page going into an autorefresh mode, and you can set an alert for when new offers appear based on your setup, if you're trying to get an item for cheap.
But generally speaking, for the casual buying stuff I do, it's super simple. Enter the name of the unique I want and hit search, nothing else really needed. Check for vendors that listed it not too long ago first as they tend to respond faster than people who listed some shit a week ago. Click the whisper button thing to copy to your clipboard, then alt tab back into game, open chat, ctrl V and as mentionned, accept party invite, go to their hideout, wait for them to open trade, drop your shit in(helpful if you prepare the currency before hand so you don't stumble like a retard and waste their time), make sure to double check what you're buying, quality, ilvl, lvl req, socket color, sometimes people will try to scam, sometimes they just have several similar items and don't pay attention.
Honestly, short of being integrated directly into the game and not needing to actually trade with people, the system is basically what you'd think when you think of an AH system.