If you only need to remove the core it just lays in place and can be removed by separating the two halves of the box. Unfortunately if the core has never been removed before the entire box will need to be removed from the car to access some small sheetmetal screws on the back side next to the firewall. You might check to see if those screws are still in place because often if a core was replaced or worked on previously they were left out so the entire box did not have to come off again.
If you need to remove the entire heater box the procedure in the manual linked above explains where the nuts holding it are located in the metal air diverter box inside the passenger compartment. A couple of the nuts are kind of recessed and somewhat hard to access. If they are rusty it may require a bit of work to get them off. There may also be additional sheet metal screws on the engine compartment side added by dealers so if the nuts alone do not seem to release the box look for hidden screws under the box or around the round vent opening that go into the sheetmetal. Once the nuts and any screws, the fabric duct and the flapper valve cable are removed the entire box and vent tube assy will lift out. Removing the small sheetmetal screws that fasten the two halves of the box together will provide access to the core. A gasket material which could have deteriorated and became sticky may want to hold the core in place but there should not be any other fasteners.