Selling:
Based on time - First come first served.
Based on price - lower priced items will sell before higher priced items.
Based on item demand - less demand means GE will sell few items from each person, and vise versa, and it will sell bits here and there.
Buying:
Based on time - First come first served.
Based on price - higher priced items will buy faster than lower priced items.
Based on item demand - less demand means you will have to offer more or wait for it to buy and if you're buying a lot you will get bits here and there.
Based on quantity - To prevent merching, Jagex implemented item limits. It resets every 4 hours. If an item has a limit of 10k, if you try buying 20k, only 10k will come in right now and the other will come in 4 hours. If you order 50k, you will get 10k per 4 hours. Prices change every now and then - I forgot the exact time they do - and when that happens, you need to update your offer in GE or your item will be outside of the price loop and won't buy or sell.
Members have an advantage because they can sell more at a time, but that's all I think it has to do.