A properly designed washing machine should have a soap dispenser drawer that comes out very easily. With the drawer fully extended out there should be something obvious at the back which you need to press down on in order to release the drawer so it pulls all the way out.
Some (especially the cheaper) washing machines don’t have anything to press down. If not try looking underneath the drawer to see if there is anything to push up which will allow the drawer to come out. With some drawers there is nothing obvious at all. Some have even been designed (especially older ones) to just be pulled out with enough force to override a small stop at the bottom.
The important thing to remember is that there will be some type of stop sticking out at the bottom or top and right at the back which prevents the drawer just falling out onto the floor when pulled out. Some used to need pulling out whilst lifting at the same time to ride over the stop, and others just needed a firm pull.
If you do decide to firmly pull it though, make sure you don’t hold the drawer by the drawer front, which will most likely break off. Hold the drawer by the sides close to the back.