Trading requirements:

75+ rep (see Exceptions).
Public Steam profile.
Steam profile must be associated with your Steamtrades account.
Steam profile must be in good standing (see Exceptions).
Steam level 1+.
Steam account must be 1+ years old.

Exceptions:

For Steam bans (meet all of the previous requirements & additionally the following requirements)
1+ year since your last game, VAC, or Economy ban (no exceptions for Community ban).
Steam level 5+.
5+ games on Steam profile.

For less than 75+ rep (meet parts of the previous trading requirements & additionally the following requirements)
You must link any rep you have outside of Steamtrades (Steam rep doesn't count).
Steam level 5+.
5+ games on Steam profile.
Rep outside of Steamtrades must have 1+ year history of trades with minimum of 30+ rep & a minimum of 30+ rep on Steamtrades (might change this in the future).

For both Steam bans & low reputation
You must meet all of the requirements.

FAQ - (Frequently Asked Questions)

Q. How can I contact you?
Comment here OR through steam (friend requests without comments here will be ignored).

Q. What is the meaning of the tags next to a game?
(Pending) next to a game title means that I'll be keeping the game for myself if no offers are made.
(Reserved) means someone has provided an offer but you're welcome to create any counter-offers.

Q. What do you mean by other games?
Steam games that I do not already own.
See this list for games that I don't want to trade for (press CTRL + F to search for a game inside of the spreadsheet).
If your offering a game, the game should have a minimum mostly positive rating on Steam.

Disclaimer:

I'm from Great Britain which utilises GBP (British pound sterling); consider regional-pricing differences when presenting an offer.
I'm not available 24/7.