According to the Platform Guidelines 1.3, you are not allowed to store a Facebook user's credentials. The best you can hope for is that your user checks the "Keep me logged in" option. She should be able to post without having to login any time soon, even if she restarts your app.
The following snippet works with the above scenario:
NSString *fbAPIKey = ...;
NSString *fbApplicationSecret = ...;
_session = [[FBSession sessionForApplication:fbAPIKey secret:fbApplicationSecret delegate:self] retain];
// checks whether session can be resumed - whether login is required
if (![_session resume]) {
FBLoginDialog *loginDialog = [[[FBLoginDialog alloc] initWithSession:_session] autorelease];
[loginDialog show];
}