On the right top corner at http://snip.ly you'll see a link to logout. Once you logout, you can log back into another account.
If you use Twitter login, there's a chance that it'll keep logging you back into the same account without giving you the option to login to a different account. This is likely because you're logged into Twitter in a different tab. All you need to do is to go to http://twitter.com and make sure you logout of there, then Sniply should let you login to a different account. Likewise with Facebook, you may have to visit http://facebook.com and make sure you logout of that account.
If you use Email login there should be no problems.