If you're new to DotA or trading in general you may not know what are the most wanted items. If you have one of them and you're not interested in it you may earn many other items you're interested in or, why not, games. Currently there are many types of items:
Items that you can drop while playing
Items that you can either buy in the Store or drop while playing
Items that you can ONLY buy in the Store but that could be droppable in the future
Items that you can only get from chests
Items that you cannot drop or buy anymore (like Vintage Timebreaker)
Promotional items (like Kantusa the Script Sword)
Tournament items that you can only drop while watching tournaments.
Strange and unusual items
Before you start you must know to what category the items you're willing to trade belong to. The DotA 2 Wiki[www.dota2wiki.com] is a good place to start if you have absolutely no idea.
2) Find the "real" price of your items
Before trading any of your items or buying a new one you always need to make sure you know the right price of them. Usually it is common to trade a rare for another rare, an uncommon for another uncommon etc but as we saw before that is not always true. There are many items which are much more rare because they cannot be dropped anymore, or because they were part of some Valve/SteelSeries store promotion which is not available anymore, or because they have a strange quality etc. The best way to find a price is ask, if you're not sure ask, if you received an offer which sounds strange ask. There are many websites where you can get a price check in a couple of minutes, I recommend Reddit but there are many:
Always remember to look for more opinions, never trust a single one, expert traders tend to manipulate the market by increasing or decreasing the price of certain items. They give false advices around forums in order to do so.
Last but not least, be fair, you can always slightly increase the price of an item but don't go too far because expecially on certain items prices are standard. For instance if you want to sell the WindRunner SparrowHawk set (which is up for 11.99€ on the Store right now) you can't ask more than 6 keys. That would be unfair and it is unlikely that you will find someone willing to trade.
3) Make sure your trader is not trying to scam you
My first advice, expecially if you're trading for your first time, is always trade items for items (or keys and games if you know what you're doing), but don't go for PayPal. When someone adds you for a trade take your time to check if he's a good user. 99% of the times he will be but since Internet is full of stupid people you'd better check.
First thing you want to check is its Steam account. If you go to his profile you can see how many games he has and how many hours of DotA 2 he played. Many scammers use a secondary account in order to gather items. They may look allright but usually they don't have any friends in the list, they have only two games, their profile is private and they have no good comments at all. That doesn't automatically mean that they're bad people trying to cheat you but in these cases you'd better watch out.
4) Take your time!
Never, NEVER rush your trade, take your time to make sure everything is correct. Once you press the big green button you can't go back so it's better to waste one minute than throw away one of your favourite items. It may sounds stupid but you don't know how many users will try to cheat you in that way. Many items look very similar so always look at their description (you can do that while overing your mouse while trading). I can't stress this enough, DON'T rush, DON'T.
5) Enjoy and "rep++"
It's a common good manner to post a comment on your trader's profile if everything went good. Something like '++rep' is enough but feel free to be more friendly. This is REALLY important because the more reputation an user have the more chances are that he won't try to scam you. Steam is a community driven network, make good use of it!
6) I've been scammed! What now? (Bonus)
Chances are that even if you've been careful enough you may get scammed anyway. In that case unless your account has been hacked Steam will not give your items back but you can still report the user who scammed you on the Internet. Report him on Steam and on most known trading websites such as Reddit.