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We can get a spacecraft to Mars using the least fuel possible using a method known as a Hohmann transfer orbit. Remember that on Earth, or in Earth orbit, the spacecraft is already orbiting the Sun. What we need to do is launch it into space with a speed different than that of Earth, so its new elliptical orbit about the sun will be larger than Earth's. We want to do this so that the orbit of the spacecraft and the orbit of Mars will intersect.
Obviously, you want Mars and the spacecraft to get to the same point in their orbits at the same time, not just cross each other's paths The spacecraft must be launched at the correct time in order for it to catch up to Mars, and intersect its orbit. Because of the different lengths of time it takes for Mars (687 days) and Earth (365 days) to orbit the sun, this window of opportunity will only occur every 25 months. Because Earth is travelling faster around the Sun than is Mars, the spacecraft will be launched when Mars is ahead, and it will then catch up.
The Hohmann transfer orbit is the least energy intensive way of going from one planet to another. It launches the spacecraft on one side of Earth's orbit, and catches up to Mars having orbited halfway around the Sun. This requires a speed only slightly greater than that needed to go into Earth orbit, so it saves fuel, but it takes a long time to get there. On a manned mission, we would likely want to go considerably faster than this. We can do this by accelerating to a higher initial velocity as we leave Earth. In other words we will have to run our rocket engines longer, which will take more fuel. However, the path of the spacecraft between the planets is still elliptical.
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When we want to return from Mars, we will also use an elliptical path. However this time, we'll launch our spacecraft at a slower velocity than Mars as it orbits the Sun. Also, remember that Mars travels more slowly than Earth, so we'll launch when the Earth is behind Mars, and let the spacecraft catch up.
If you would like to learn more about the physics of interplanetary travel, click here.
