There's a few ways to do this. If you just want to quickly check snapshot of prices without regard for the economy of your particular server, just check Wowhead.
Wowhead displays the items vendor value, as well as the average auction buyout price across all servers.
However, this information is sub-par in that not every servers economy is the same, and in fact substantial price swings occur across realms. Also, for items that are less frequently traded, there may be little to no data.
If you want a more detailed picture, you need to go to the source from which WoWhead derives it's average; The Undermine Journal by contrast, provides a much more comprehensive picture, giving you price history and current pricing data for any item, specific to your realm and faction, as well as the cost of component materials for crafted items, should you wish to just produce them yourself or ask a friend to. Additionally, TUJ distributes an add-on that will allow you to view historic data for an item in game while browsing the AH.
As you can see from this screenshot, The Undermine Journal is far more detailed, as well as providing a more specific and accurate picture - for instance, the item in question (Flask of the Winds again), is roughly 30% more expensive at the Ysera-Alliance auction house than Wowheads average across realms indicated.
(European players will note that TUJ EU site is found here.)