Start by looking at the error log
tail -15 /var/log/apache2/error.log
If that doesn't give a hint such as ports being unavailable or so, run
apache2ctl -t to test your config.
If your config is good, check to see if any process is already bound to port 80 or 443 (which is probably the ports you want apache on). The last column of the output will be $PID/$process_name.
sudo netstat -tlpne | egrep ':(80|443)'
Alternatively, see if Apache is running but listening on other ports...
sudo netstat -tlpne | grep apache
If you still haven't sorted it out by now, it wouldn't hurt to check that Apache is configured to the domains you expect, so run
apache2ctl -S and you should see a list of configured domains. If your domain/port combination isn't listed there, you'll want to sort out your config.
There're more still, but these will reveal many common configuration problems.