There are many different options for purifying water. The easiest options is to buy a portable water filter. Most of these are manual pump systems, some good brands are katadyn or msr. There are also Steripens, which use uv light to purify water, and are very quick, although they do not filter out sediment, only kill bacteria. Water purification tablets work also although they are not 100% fullproof.
If your looking for a do it yourself option you can always strain the water through something like a coffee filter, or even your sock if your desperate, and then boil the water. It should be purified once boiling, although if you went for the sock option then it may not taste that wonderful.
Hope this helps!