Getting clean water in the backcountry is not difficult (at least in the Northeast). But, there are a lot of different ways to do it. Here I will give you a breakdown of those ways.
But first, let me explain why you should never ever drink water without treating it.
In a sentence, if you accidentally drink animal poop, you will poop, A LOT.
In a more complicated explanation. Giardia is a very common infection caused by the giardia lamblia parasite. The parasite is present in water contaminated by feces (from all the deers, and moose and stuff). The Giardia parasite sets up shop inside your intestines and causes you to have watery diarrhea.
The old adage (think back to "Of Mice & Men") is that if water is moving it is safe to drink. Just like many other "old adages" this turns out to be completely untrue. You might be sitting at the edge of a flowing river and all looks swell and dandy, but just around the bend there is a deer relieving itself into the water you're about to put in your body... or worse.
If that is not scary enough, remember, you are in the backcountry and now you are incredibly dehydrated because your body is just firing all your water out the back end (literally). The only thing you can do is hike out while continuing to drink more unclean water, which is then "fired out the back end" of your body. Thus placing you into an infinite diarrhea loop.
1. Carbon Filters
Carbon filters are very common and reliable. Typically a pump mechanism pulls the water directly from the stream through a hose, the filter, then into your bottle. Carbon filters are fast and effective, but they can be on the pricier side. Look for Sawyer Filters, or the Katadyn Filter.
Pros: Reliable, sturdy, replaceable filters.
Cons: Weight, Packability, Time
2. Chlorine Tablets
Chlorine Tablets are available at most outdoor retailers. They work great when dosed correctly to the amount of water you are purifying. The only downside is you could run out, or constantly need to buy more. This is obviously not an issue with carbon filters.
Pros: Packability, Size, Weight
Cons: Finite amount, Dosing instructions
SteriPens are one of the most recent developments in purifying water technology. Essentially you collect your water and then blast it with Ultraviolet Light until everything is dead inside of it (pretty ultra violent if you ask me). This process wipes out all of bacteria, but can leave in sediment and other physical particles (think mud, silt, leaves). It is a pretty cool piece of tech, but has downsides including reliability and lifespan.
Pros: Small, Light, Super effective at killing bacteria
Cons: Breaks easily, Battery life, Less reliable, Price
4. Iodine Droplets
If you like to keep it old-school bring along some iodine. The most common system is a glass bottle with "Iodine crystals" in the bottom, you add water to the crystals and that makes the solution you then use to purify your water. As long as there are still solid crystals you can continue filling the glass container over and over making more purifying solution to add to water. Iodine has gone out of style mostly due to the metallic taste it adds to the water and the sometimes complex purification system. The number of drops of the solution need is dependent on the amount of water and the waters temperature which also effects the amount of time it takes before the water is potable.
Pros: Super effective, Packable, Old-school, Reliable
Cons: Taste, Sometimes complex process, Waiting for purification