Hi,
There are at least two approaches.
You could tick the Allow custom text entry in the Object > Field palette:

This would allow a user to overtype directly into the dropdown. Their input does not become an item on the list.
Another approach would be to have script in the exit event of the dropdown which would show a textfield if the user selected Other from the list. For example if the text field was called otherDescription, then this in the exit event of the dropdown should work:
if (this.rawValue === "Other") {
otherDescription.presence = "visible";
}
else {
otherDescription.presence = "hidden";
}
Hope that helps,
Niall