One of the best ways to motivate your team is to be motivated yourself. When your team sees your motivation, it'll rub off on them (to varying degrees on different team members). But being motivated yourself is only the first step to motivating your team, there are many other factors at play.
Another big factor that comes into play is the work environment. People tend to be more motivated when they're comfortable in their environment. If people are friendly towards one another, work well together, and have personal relationships with each other it'll create a positive environment where your team members can push each other to do their best. Some ways to help your team to strengthen their relationships with each other include holding team lunches, recreational activities, team building exercises, and other team events where people can interact outside of the work environment.
A good way to help motivate your team is to set goals and create challenges for your team. When people are working towards a goal they have something to focus on and strive towards. You could establish two different sets of goals, one for the team and another set of goals for each team member. If one's work becomes mundane and uninteresting, it is a good idea to give a more challenging assignment to that person. Also splitting up the team into smaller groups and setting up a friendly competition between the groups to see which team is able to produce the best can easily stir up motivation within the team.
One of the easiest ways to motivate your team is to be appreciative of the work they do. A simple "Thank you" or "Please" can go a long way. Also giving praise for a job well done can be a huge motivator. If team members know that there contribution is appreciated, they'll work harder. Awards and incentives given out for performance or after certain goals have been met (to the entire team and/or individuals) is another way to boost motivation. Just keep in mind that no two people are the same so different methods of motivation will effect different people differently.