The idea is to use a simple branch based on a match on the 'Other' option. In case a respondent selects that option, a follow up question is shown. In most cases this will be a text input field, so the respondent can enter its own answer.
We have made a video tutorial on how to add a branch for an 'Other...' option. It's a tutorial on simple logic, which shows what steps to take to get this done.