Depends alot on the daemon.
If the daemon has an API and you can communicate to it via either a TCP/IP socket, or a UNIX socket, then you can do that.
If it listens on a TCP/IP port for example, you can write a script that connects to it, expects a certain response - and also times how long it took to get that response - you can feed that to monitoring tools such as nagios, munin, or other - Whatever script you end up writing to carry out a single check, you can then easily integrate into nagios plugin for example - which is probably what you want to do - once you've written your check script.
If it provides you nothing useful, does not listen on a port, all you can really do is check the process tree using lsof, netstat, or something like that, and just make sure it exists, but you can't really do a health check.
You'll need to be more specific really before anyone here can offer you something useful.
Have a look at the PID of the running daemon, then look under
/proc/<PID>/fd to get a view of what pipes/sockets/files the daemon is interacting with - that might help you get started.