What format are your designs in? If they are in vector format, you can verify that the vector art is closed loop and then cut them directly. If it is not in vector format (JPEG, Bitmap, etc.) then it will need to be vectorized.
InkScape is free and has vectorization built in. You can also vectorize with Corel Draw, Illustrator, DragonCut, Flexi Sign, VinylMaster, etc. Then, once your image is vectorized you can cut it in heat transfer material like ThermoFlex Plus and press it on a shirt.
Alternatively, you can print your JPEG designs on sublimation paper and press them onto your shirts directly maintaining the full color scheme without the need for vectorization.