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Assess the abilities of those you supervise. If you have some experience on the same level of hierarchy, draw on your observations from then. Look at both the work output and the interactions and relationships between different workers.
Make a personal list of the strengths and weaknesses of the company. Include general ideas, such as consistency, as well as things related more directly to your particular department. Don't censor yourself. Understand your job, but also its relationship to your company as a whole.
Assess the need for change. Sometimes, a company needs a radical change from a new supervisor. At other times, the best thing to do is to maintain the status quo or continue progressing in the same direction as your predecessor. Don't shake things up just to look bold.
Keep things on an informal level. Just because you
are a supervisor doesn't mean that you have to artificially put distance between yourself and your workers. Avoid the temptation to overtly redefine your relationship with your coworkers.
Delegate work, then step back. Assume that everyone knows his job. Simply assign projects and wait for results. Most people produce their best work when given the autonomy and respect that they desire as adults.
Step in dispassionately to correct errors. If someone does not seem to understand a project, or has fallen behind a deadline, step in to help him out. Discuss the needs of the project and what needs to be done, rather than shaming, threatening, or appealing to loyalty or personal friendship.
Offer praise, both to encourage and to reward good work. If someone struggles with a project, praise him when he gets it right. If another worker excels, praise her to recognize her accomplishments.