How to turn froth into juice?

I have the brand of juicer (Champion) mentioned by the OP in comments. It's a rather unusual design that isn't used by most other companies. They are somewhat notorious for producing a lot of foam. I bought it perhaps 15 years ago, but rarely use it for this reason. (It still has other uses other than juicing.)

Anyhow, the solution I found to this problem was simply to strain the juice through a fine-mesh sieve. It won't go quickly and will get clogged with the pulp, so you'll need to a take a spoon or something and stir it around to force the juice through. It takes a long time, but it's effective because the bubbles dissipate when they go through the sieve. Given the construction of these types of juicers, I would generally just place a bowl underneath and a large sieve in the bowl to catch the juice coming out. After finishing juicing, you can turn off the machine and then spend 5 minutes stirring and straining to get rid of the foam.

I have seen others on the internet mention success using a French press to do a similar straining action to destroy the foam. I tried it once but it didn't seem to work as well (perhaps the stirring action within the sieve also assists with the foam). Nevertheless, it still made an improvement.

I haven't tried this, but in theory, it can work:

Try adding a couple of tablespoons of flaxseed oil, coconut oil (or any other healthy oil you'd drink) to the froth jar and swish around. It'll likely destabilize the foam.

Additional Info: Foams are similar to emulsions and are usually caused by proteins. Many industrial processes use surfactants to destablize the foam. This article is a primer on de-foamers. Aside from vegetable oils and milk fat, you may find most of the defoaming chemicals contradictory to the nature of your juicing.

Alternative approach: a high-speed blender such as the Vita-Mix will incorporate less air into the juice (since the blades are submerged) compared to a traditional juicer machine and result in less foam. Also, for vegetables such as beets and carrots, it is significantly better to ingest the fibre (per blender method) as opposed to through it out.

Food grade antifoam.

There are a zillion brands. Looks like most are silicone based.

The speed of your juicer might be very high, for example our commercial juicers are 3,000 RPM's and that does not yield high levels of foam. Some home juicers have RPM's as high as 12,000 - 14,000 which will cause a lot of foam. Another tip to reduce the foam is to make sure your greens are fully hydrated, possible keep them in a bowl of water as you are juicing them.

Year later, but I'll respond. There is no special trick. Use a skimming spoon to get the thick foam at the top. When you get to the foam that falls through easily, stop straining. The rest you can just stir into the liquid. Stir, wait a few minutes... repeat.