How do I avoid airlock foam overflow? Does it affect the fermentation process?

Just be careful with using the Blow-off hose thru the airlock as you might get a clog from the hop stuff in the Krausen. Just saying... I thought it was funny when the airlock blew off the carboy the first time I tried this method. The simple fix was to cut the end off the airlock, to free up some space and eliminate those four little holes at the bottom that I call cloggers... One snip, reattach the hose, worked like a charm...Use it for a couple days, replace it with a butler after that... no worries. And yes, watching that blow off hose work is really cool as all he77.

Personally I always use a blowoff for the first 48 hours (just in case). Then add bubbler after things have settled down. While your risk is minimal for infection, the critical time is between the development of the krausen and presence of alcohol.

Just making my first batch. Filled the first Carboy up too much. Used a racking tube through the bung and attached plastic siphone tube to that and ran it into sanitizer container. Working like a charm.

Scott's answer is correct. And I've done this as well, both on my last batch, and the previous one (in which it actually overflowed twice). The blowoff tube is the best approach; I misplaced mine, so I had to do without, and like yourself, I just changed it out and went along my way.

You could prevent this all-together by leaving more headroom in the carboy, or making a beer with a less fervent fermentation process. But what's the fun in that?

I am not expecting anything bad in my batches where this happened. Unless there was beer sitting in there for an extended amount of time, I would think it will be fine.

Headspace in the carboy is nice to avoid this, but ultimately, a blow-off tube is the answer. By switching out the airlocks, you did the right thing, and ultimately, as long as you didn't let it sit exposed for a long period of time (in the realm of 20+ minutes), the likelihood of infection isn't high. Plus, the krausen (foamy stuff that sits on top of the wort while fermenting) acts as a protective layer from bacteria. By the time the krausen dies down, the bacteria will come in contact with alcohol, lessening the chances for infection (hopefully).

Simplest way to do this, take apart a 3-piece airlock, determine the diameter of the inner tube that feeds into the bucket (I don't know the diameter off the top of my head), and get about 3-4 feet of tubing that size. Plug one end of the top of that inner plastic tube of the airlock, fill a bucket, or some form of container with sanitizer, and put the loose end in the sanitizer completely submerged. Now, if anything comes out the top, it simply goes into the container, no bucket/carboy-bombs.

EDIT: Visited the LHBS today on the way home to get my next recipe. You want half-inch (either thin or thick wall, both will work) hosing, at least 3 feet, ideally 4, for your blow off tube.

By the way, this is very common. The investment of a blow off is well worth the cost. Seeing yeast shoot out of the carboy (ideally through a blow-off tube, but any way works, albeit a bit messy without) is one of the most fascinating parts of brewing.