I think you've got it. Look at the image below (from the MGS website):

Each of the dots on the orbits represents a 30 day interval. Notice how the Earth's dots are further apart than the Mars dots. That's one way of showing that the Earth is going around the Sun faster than Mars. To fly from the Earth to Mars, your spacecraft has to accelerate (relative to the Sun) to raise the apohelion to reach Mars. As your spacecraft gets further from the Sun, it'll be slowing down the whole time.

Likewise, to fly from Mars to the Earth, your spacecraft has to decelerate relative to the Sun to fall into a lower orbit. As your orbit gets closer to the Earth, the spacecraft will be gaining velocity the whole time.

The same things we discussed about orbital velocity and altitude apply to rendevous and docking, too. Suppose the spacecraft you want to dock with is 400 km in front of you. If you fire your thrusters to accelerate, you'll actually climb to a higher orbit and end up going slower, so your target gets further away. Instead, you'll need to do a retro burn to slow down a bit, dropping into a lower orbit, so you can go faster and catch up. As you get closer, you'll want to boost your orbit to reduce the relative velocity. At the moment of docking, you need to be in precisely the same orbit.

Gee, this sounds like rocket science! Thank goodness for computers and the really bright people who program them to accurately fly these trajectories. Now, throw in tricky things like gravity assist slingshot maneuvers around planets.

If you want to see the math behind an Earth-Mars Hoffman transfer, here's a link to a student presentation (from MIT). The basic math really isn't all that hard, but the detailed trajectory calculations are.