"Trusted" is a subjective matter. You're probably not trusted with someone's account that has 500M on it right now because you have no trading history.
If you want to be trusted with handing people's accounts (e.g. transferring gold, questing, skilling, goldfarming) or fulfilling trades honorably (e.g. selling an item for cash), then you'll have to build up a history of using people's accounts and giving them back, or by simply completing trades. What smytheroo said (doing some free training on low-level accounts that have low risk) will get your foot in the door, but ultimately you have to show that you're able to handle higher-leveled accounts or transactions as well. People don't really care much about the "work" you have done on sythe as much as how many accounts have safely passed through your hands.
If you want to be trusted in account sales, you'll have to start selling accounts. Account sales is generally more lucrative because it's very easy to recover a sold account, so it takes highly trusted members. It's best to start here with low-leveled accounts, since people are reluctant to pay $100+ for an account to someone who could easily recover it back. Since you can't sell an account without any trust, you'll need a middleman (someone who has the trust to handle the trade for both parties), which costs a fee.
Eventually, with enough trade history in either side, you'll be considered universally trusted. This means that your reputation on Sythe as a seller/buyer is generally enough so that it is believed that you will never risk being banned being caught in a scam.
EDIT: It's important to keep track of your trades, too. Set up a vouch thread in the
Vouches Forum to keep track of who you have dealt with. Be sure and read the rules of the forum to keep the format up to standard.
