I need to crimp the 18 awg wires into the 3-pin female JST VHR connector, but have no clue as to how to do it. How would the crimp latch onto the JST housing? Can somebody point me to any helpful resources? Thanks!
You already have an answer apparently pointing out the "proper" tool, which you could also determine from manufacturer guidance.
If you only need to do a few for prototype use however, there are more universal manual solutions, such as the Engineer PA-09 and PA-20. These require some degree of skill and experimentation to produce acceptable results, but are a pragmatic solution when you have more variety than you can justify having unique tools for.
Apparently official removal tools are expensive. A small jeweler's screwdriver makes an unofficial one, be careful not to bend the locking tab too far or you may have to bend it back and/or replace the contact.
You appear to have stripped far too much insulation, typical connectors crimp once on the bare wire and then also just past that over the insulation, but details vary - and vary even more if you end up needing to improvise with an official unsupported wire size.
Ultimately what the best solution is depends on the volume and requirements of your need...
You could get the crimper and put terminals directly onto the wires you have; the part number is WC-930 and it's almost $500. Or, you could get pre-terminated jumpers from Digikey, et. al. and splice them onto the wires. They're less than $1 each. The contacts have a little tab on them that latches into a notch inside the connector housing. Just don't screw up the wiring since the extraction tool is $200.