There are 3 places you can acquire your items.
The Fountain:This is where you can get most of your items, if your inventory space is full or you are not at the fountain, the items you purchased are put in a stash. You can have the courier put items from your stash and deliver them to you.
Sideshop: These are located at the far left top lane, far right bottom lane. You can acquire SOME items from the secret shop/fountain, this means you don't risk your courier getting killed.
The (Not-so) Secret Shop: Located between mid and top for Radiant. Mid and Bottom for Dire. There are exclusive items bought here( usually for late game items) expensive and give great stats.
Items are given a price next to it in the shop menu. On how to acquire gold watch this video