First, here are my OpenVPN configuration notes as a general starting point.
And here are the OpenVPN docs about bridging.
The short answer is that if you set up a bridged openvpn config and you use a split tunnel, the clients will be directly connected only to the server's network via the vpn. If you want the clients to be able to connect to other networks beyond that on the server side, you need to push one or more routes to them via the vpn.
If you don't use a split tunnel (all traffic goes through the vpn, via the redirect-gateway setting), then you can use the dhcp server config to push a default gateway to the hosts, and they can use that (over the vpn) to get to other networks, or out to the internet. You also need to use an iptables nat config as detailed in the docs.