The answer to this really hinges on how long it takes for the applicant to get the relevant information needed to submit an application. Usually, from the moment that all the materials have been given, an application can be filed, prepared and submitted within weeks. If ever there is delay, such is due to the time it takes to get the certification of the Labor Condition Application from the Department of Labor, as an H-1B visa application must be filed with the approval by LCA.
Corollary to this, the time depends on the USCIS and the process and approach of filing. If the application was deemed filed by using the regular processing, it can easily take three months at the least. However, if the application was submitted through premium processing, then such can take up to half a month.