If you are currently in another non-immigrant classification (e.g. F-1, J-1, H-4 etc.) and are changing to an H-1B status, you will need to wait until USCIS approves the H-1B petition before you can begin working in H-1B status.
Some individuals who are in the J status are subject to a two-year home country return requirement called 212(e). If so, you will need to apply for a waiver of 212e or have served the 2-year requirement before being granted H-1B status. Applications for the waiver can be done concurrently while your H-1B case is being prepared. However, final approval from the Department of State showing that you have received the waiver must be included with your H-1B petition when it is submitted to USCIS. Timing of the waiver application should be carefully considered since it may impact your current situation. Speak with an OIA Immigration Coordinator/Specialist about the waiver process before you apply. You may also get more information at Immigration Restrictions.
If you are currently on F-1 OPT, you may also be eligible for additional time on your OPT if you are in one of the STEM (Science, Technology, Engineering, Mathematics) fields. See Stem Extension OPT for more information.