You can do this in two ways. On the profile page immediately after logging in, you can set the option "Make your order list private". The site will then only show your open and closed trades while you are logged in to the site. If you are not logged in (or someone else is visiting your results) then the site will show statistics, but not individual trades. Please note that this setting prevents the mobile version of the site being able to list your trades.
Alternatively, you can turn off publication of open trades and/or pending orders. If you are publishing your results using one of our publisher apps, then you set this option in the app (e.g. you turn off the IncludeOpenOrders parameter in the MT4 publisher EA). If you are publishing your results using account sync, then you turn off the equivalent setting on the account sync page.
If you turn off publication of these trades then they are not visible at all on the website at any time. The website simply does not receive this data. The information is not displayed - because it is not available - even when you are logged in to your account on the website.
A further option is that you can set a delay on publication: orders are only included N minutes after they are opened. This option is available in all our publisher apps (e.g. the DelayTradeListByMinutes parameter in the MT4 publisher EA), and on the account sync page.