To propose a trade within the game, click Trades on the Manage menu. The Manage Trades screen allows you to review trade proposals made to your team, or propose a trade to another team.
To propose a trade use the drop down menu to select your trading partner. Once selected, that team's players, salaries, and remaining starts will display. Click the buttons next to the player(s) you want to receive and trade away. If you are receiving more players than you're giving you'll also have to click the Release button next to some player(s) -- rosters cannot be greater than 28 players. You can have more than one trade proposed to you but only one proposed by you.
Enter cash amounts at the bottom of the screen and then click the red Propose This Trade button. Once BBM receives the trade offer it will be posted at the top of the page. It is advisable to double check those details! Both teams will receive an email immediately after a trade is proposed and the words Trade Pending will appear on the Homepage of each team.
An example: The Hungry Hippos trade away one player whose salary is $2000k and receive 2 players from the Wild Turkeys with combined salaries are $800k. If no cash were involved in the deal, the remaining payroll of the Hungry Hippos would increase by $1200k and the Wild Turkeys would go down $1200k. Many managers don't want their payrolls to change... they just want to exchange players. In that case, the teams would include the difference in salaries of the players (in this case the Hungry Hippos would include $1200 as part of the trade).
Trades are instantly processed in leagues not using the trade review process. Once a team accepts a trade the players (and any cash) will immediately change teams. The players will appear in the Inactive Players list. An email will be sent to all the managers in the league announcing the trade.
For leagues using trade review the process is a little different. [See Trade Review]