So when I place a buy order for say 1 share will I own that share instantly or do I have to wait for it to be filled by someone? The same with selling, if I place a sell order will they be sold instantly?
The exchange matches buyers with sellers. If you place a buy order for a particular price (called a "bid") and there is already a seller that has placed an order to sell shares (called an "ask") at that price, then you will immediately buy from that seller. If there is nobody selling at that price, then the exchange will save your buy order, and later when there is someone that wants to sell shares at your price, his shares will be sold to you.
That's it in a nutshell.