It greatly depends on the security configuration on the target computer. I will suppose for all this that we're speaking about public IP and attacks over internet (not LAN).
At the very minimum, you can ping it if the router it's not configured to reject those. This open a clear route for a DoS attack
(or it's distributed twin, the DDoS), which can make the connection of the target quite slow or totally unavailable if your bandwidth is greater. That's a quite common way for hackers to take websites down.
Then, you can attempt a port scan
to discover open ports and listening services on that host. If there's something "alive" there, there is a chance to find something with a security vulnerability, a weak password or just to flood with dummy requests.
All that of course relies heavility onwhat do your find and how many security vulnerabilities are out there. A properly secured computer will most likely not have much to do, and for sure it's not a straigforward way to break into someone else computer, much less to completely take control of it.