Teams must tender a contract within 15 days of the draft. Usually this happens by FedEx delivery. But this will just be the standard 7-year form, no bonus involved. If there are bonus negotiations, it's like any other case of negotiations, it can go fast or slowly depending on whether the two sides see eye to eye.
In some cases, there are no negotiations. If a player was considered "unsignable", things may never get beyond the required contract tender hitting the circular file upon receipt.
August 15 is the new deadline that took effect under the collective bargaining agreement changes that took effect in 2007. Sign by then or become a free agent. If you set foot in a 4-year college classroom, however, you're off the market until 2011.