In an organization that you are very new, how do you manage a project and it's personnel assigned to you?

learn as much as you can about the organization, then find the link that you can use to attach to. 

Then, set your self and be a leader in your work; i.e do the job and let people follow.

and as any other manager, by strict yet very respectful to your team and always appreciate the good work. 

You should know the Enterprise Environmental Factors & Organizational Process Assets of the new company to deal up with a new project assigned to you. To manage people of your team, you should perform team building activities, know their interest, requirement & expectation from the project. Get them trained for any new skills. Adopt a reward system etc 

Study old projects results, process and LEARN, LEARN AND LEARN.

You are your position and experience...there is nothing new in any project..make drawing or study drawing estimate man,material and time..plan and schedule..start work..

Being new to an organization, it is important to try and learn the "ropes" and the company's culture. Also, one must trust the team one is managing, delegate and make accountable for the tasks in hand. Also, one has to step up and stand for the choices and decisions made; failure to comply to a company's standards or procedures can be accepted if the best effort was put to complete the task, and such failure can be attributed to not fully knowing those procedures.

This is basically a question of "project management" and "human resources management" within the context of project management. Being new to the organization could work well against you specially when things go wrong. It may also work for you for a very short period that I call "window of opportunity".  This is where you still try to learn/adopt to the new environment, and the people/management gives you the chance to do what is expected from you. Another important factor here -being new to the organizatio-,  is the terms of engagement (duties, obligations, authority level, ...) that is assigned to to you and you accept as basis for fulfilling the expectations and delivering what is needed/expected from you.