Good filtration is absolutely key for maintaining a healthy tank. There are many filtration options, but first you will need to understand your tank's ecology. Before reading this section, go read about the nitrification cycle.
Types of Filtration
There are three types of filtration: Physical (foam pads), chemical (carbon pads and zeolite), and biological (ceramic rings and bio-wheels).
Since the nitrates will build up in the tank, water changes are a must. However, a full water change will throw the tank parameters off and start the nitrification cycle all over again. Instead, do small water changes. 20% every other week or 10% every week are common amounts. If the tank is particularly dirty, do 10-20% every day, but don't take out all of the water.
To do the water changes, it's easiest to use a syphon. You can either purchase one or build it yourself.
How much filtration does a turtle need? Figure on twice that which an equivalently sized fish tank needs. Turtles are extremely dirty animals!
There are four main styles of filters: power filters (over-the-top), undergravel filters, canister filters, and wet/dry filters. Do not purchase filters labeled as "For Turtles". These are notoriously underpowered and overpriced!
Power filters are the common style of filters used for fish tanks. However, these filters are inefficient as the main filter unit in a large turtle tank. The advantage of Power Filters is easy access to the unit, so it's very quick to change carbon pads. Many turtle owners use these as a secondary or "polishing" filter for carbon and extra biological filtration. They are also useful for small feed tanks to raise snails and fish.
These filters are pretty much useless for turtles. They are underpowered and expensive. Besides, turtle tanks shouldn't have gravel.
These are the most popular filters for turtles. They are more efficient than power filters. The entire unit must sit below the tank (18 inches below the water line). The canister is a closed unit with intake and outtake tubes that go back into the tank. Inside the canister are trays for physical, biological, and chemical filtration. Many people use only physical and biological filtration in these units so they don't have to open the filter up very often (some people report not having to clean the filter for 9 months!) A good canister filter will run at least $100 online. The benefit of these filters is that they do a good job and are easy to use. The downside is that they are a little pricey.
Wet/Dry systems are the most efficient filtration systems. They need to be below the water line, but they don't need to be 18 inches below. The water from the tank cascades over a pile of biological media, usually bio-balls. The extra oxygen from the balls being out of the water helps the bacteria to grow on the biological media. The water flows into a small holding tank before it is pumped back up to the main tank. Although a ready made system is quite expensive, these filters can be homemade very cheaply, and the sump (the small holding tank) can be used to grow food for your turtle. The downside is that they do require some knowledge to set up, so many first time aquarists are nervous to try these systems. They are more common with experienced aquarists.