Unless you have one, YOU are the project manager.
When choosing a General Contractor, several key points come to mind:
1. Accurate drawings are important to communicate the scope of work with finishes and details. Make sure that all of your design ambitions are clearly represented in the set of plans. Don't rely on verbal communication. Drawings are legal documents used for contractural agreements. It is important that they are comprehensive.
2. A written scope of work which outlines the entire process of construction is also important for clarity.
3. An experienced contractor is important. Verify the credentials and get a list of references from previous clients.
4. Analyze the contractors proposal including how fee payments, change orders, substitutions and requests for information during the project, will be handled.
5. Set up a construction schedule and have a weekly meeting to review progress and any items which may adversely affect the budget or deadlines.
6. Finally, work towards having open communication with you GC. It is important that you feel comfortable with your builder.
The process of construction should be a predictable process with few surprises. If your project is a large one or there may be some unknowns, then allocate 10% of your budget for contingencies which will cover any additional expenses which may arise.
In my experience with General Contractors, the most important element of the relationship is that both parties are clear about expectations. Using the elements listed above will ensure a smooth construction phase.