You will need a VOX circuit, and optionally, a VOX program. As long as the radio you are connected to is type certified, it is perfectly legal to connect it to a PC for the purposes of transmitting voice.
First off, you need some aux cables, and if you PC has a combined speaker and mic jack, you need a TRRS splitter. You also may need a 3.5 mm to 2.5 mm adapter since most HTs use Kenwood-style connectors.
For the VOX circuit, either get a soldering iron or a breadboard, and construct one of these. Your power supply needs to match the specifications (+9 to +14 VDC), and you can use a 9V battery if you don't have a power supply. You can connect your computer to the "MIKE INPUT", and put another jack in parallel with the vox circuit to connect to your radio.
In Kenwood-style connectors (which, from my research, your radio has), the radio is told to transmit when the two "ring" conductors are shorted together. This can be done through the final transistor on the right.
If you have no idea how to breadboard, you can shell out and buy a SignaLink. You plug your PC into the SignaLink via USB, and plug the radio into the audio jacks. Once you configure the SignaLink, you need to configure your PC to send your microphone audio to an output device (in this case, the SignaLink).