First and foremost thing you need to do is to make a list of the characters you need for your movie. Read your script thoroughly and write down all the characters and the details about their personality.
Keep your budget in mind otherwise you will have to compromise on the production quality. You should allocate a specific amount for your actors and then start hiring. However, if you have a unique script then there is possibility that big names will work for you even if you pay less.
If you are doing it on your own then this hiring process requires a lot of time and attention. Things can become a lot easier if you hire a casting director as they are the ones who are responsible to find right men for the job. These casting directors always have contacts with talent promoters and management agencies. Ask your casting director to call actors for auditions and shortlist few of them.
Acting schools, community theatres and performing art academies are the best places where you can find really talented actors. The best thing is these amateurs will not charge you much and they will work with more passion and devotion. Organise a talent hunt in your surroundings and trust me you will be not disappointed.
Sometimes, you can find the right person for the job even in your team. It happens all the time that a below-the-line crew member becomes a really good performer. Similarly, you should look around you in family and social circles. Even if they are not familiar with the trade, allow yourself to explore them.
Another way to find actors for an independent movie is to advertise in local newspapers, TV channels and websites. Paste your ad on the notice boards of community theatres or acting schools and you will be amazed to see the response.