How to create dynamic select option field in webform module
Go to Modules > Webform and see what version it is. If it is version 4+, as RoloDMonkey has mentioned, than conditionals are built in. If your Webform module isn't 4.x then I suggest updating it so that you can use this feature.


Go to Content and find your webform and open it. 
Click "Webform" tab
Click "Conditionals" link
Click the (+) button
Implement the logic:


If "[select question that has the conditional answers]" is "[select name of answer that opens the textbox]" then "[name of textbox]" is shown
If "[select question that has the conditional answers]" is "[select name of answer that opens the selection menu]" then "[name of selection box]" is shown.



Make sure you have all possible options set up already in the webform before applying the conditionals.

Here is a demo someone built using Webform Conditionals:
http://www.sixmiletech.com/node/15