Scrub the bottom with a scrubby on a stick, get a water filter and make sure you keep it clean.

Perhaps a filter like those meant for fish tanks. Keeps the water clean without chemicals.

You can buy an ultra-violet (UV) water purification unit that will fit between your pump and water outlet. The UV light will kill all bacteria and algae keeping the water crysal clean. There are no harmful side effects to the treated water... http://www.tmc-ltd.co.uk/pond/uv-clarifiers.asp

If you want to let your dogs drink out if it the only thing you can do it keep it clean. Give them an alternate water source, and you can put chlorine in the water.

Make sure your filter is clean and working properly

I had the same trouble with a fish pond. I created my own filter, which works wonders. You can buy the gear from a Hardware store. Get a big, square plant pot, make a hole at the bottom for the water to come out of. Purchase two or more inline particulate water filters with 13 or 19mm connectors, a good length of 13 or 19mm plastic tubing and elbows, tee joins, end stoppers, etc. and an inline tap. Get some volcanic rock - that good porous red stuff works fine. Get some activated charcoal, if the hardware store hasn't got it, an aquarium will. Get some common non-scratch scouring pads. Get some filter culture from your aquarium (good bacteria that breaks down sludge) You'll also need a pump with a 13 or 19mm attachment. The goal is to create a multi-stage filter. Firstly, the water needs to pass through the particulate filters, that'll remove the clumps and lumps. You'll change these every week or so, more in summer. After that, the water flows into the top of the plant pot, through the scouring pads, through the volcanic rock and then the activated charcoal. Finally, the water is returned to the pond through the hole in the bottom. Use the pressure of the pump to drive the water through the particulate filters, then let gravity take the rest. The bacteria is added to the water every week until a good culture has started. What you'll end up with is a natural alternative to UV or high-pressure filtering: The large surface area of the volcanic rock and activated charcoal allows the bacteria to thrive and break down a lot of the crud in the water. Note that it takes about three weeks to get a good culture started, but after that all you'll really need to do is clean out the particulate filters. Also, add some water borne plants: They'll compete with the algae for nutrients. Make sure, though, that any you do add to the water are not considered pests in your area, and if you suspect they are, don't let any get into natural waterways.