You just need an action on the entry field that does Modify Variable action with Target being the question variable, Type is Set Equal To and Value is the entry field variable (eg: VAR(Entry_73)). Trigger for that action is Select/Change, which is the default. This will set the question variable with the contents of the entry field the user types in and this value will be posted to the server.
Additionally, you can add actions to each of the radio buttons so that only when they click on “Other, please describe” the entry field will be shown. Clicking on other radio buttons will hide it.