It is up to the employer or host institution to apply for the work permit at the UWV. It takes at least 5 weeks for the application to be processed. Employers who hire foreign nationals without first obtaining a work permit risk being fined. A work permit is free of charge.
Regulations concerning work permits and immigration procedures are very much intertwined. A Schengen visa or (provisional) residence permit will be granted only if the work permit has been issued. This means that if your employer needs to apply for a work permit, you should calculate some extra time (up to 5 weeks) for the immigration procedures.
The authority for issuing work permits is called UWV. The authority deciding on (provisional) residence permits is called IND (Dutch Immigration and Naturalisation Service). Sometimes it may be possible for your employer to submit a joint application for both a work permit and a (provisional) residence permit. Both applications will then be handled at an office where these two organisations work together. If this is available in your case, we would certainly advise your employer to do so. This will save a couple of weeks time.