If the dump1090 version you are using has an option for an integrated webserver, use that.
Then in a webbrowser you should be able to navigate to http://localhost:8080 if you use port 8080 for the integrated webserver.
Most people here use a Raspberry Pi to receive and feed the data.
A map is also accessible via the local network, it looks like the picture below.
PiAware - build your own ADS-B ground station for integration with FlightAware - FlightAware
Almost forgot, you might want to checkout VRS, you should be able to connect it to the dump1090 you are using. (http://www.virtualradarserver.co.uk/)
I personally don’t like it much though.
I’d recommend tar1090 which i have developed on the basis of the dump1090-fa interface, but it’s only for dump1090-fa or readsb, which both run on the Raspberry Pi (or any debian/Ubuntu really).
GitHub - wiedehopf/tar1090: Provides an improved webinterface for use with ADS-B decoders readsb / dump1090-fa