In 2015 it was believed that the observable universe contains 100-200 billion galaxies; in October of 2016, some new applications of mathematical modeling to the Hubble deep-space images produced a new estimate of 1 trillion to 2 trillion galaxies
But that may already be out of date, as last year a study stated that there are more than 10x more galaxies than previously thought. Nearly 2 trillion of them in the observable universe!
No one knows. If you look in any direction in an area of sky the size of a dime held at arm's length, you'll see tens of thousands of galaxies. James Webb will use infrared, and will be able to see 1,000 times further. So I imagine we'll be seeing the very first galaxies within the next year or two. But to answer your question, there's no way to make an accurate guesstimation. There could very well be trillions in the observable universe.
According to the best estimates of astronomers there are at least one hundred billion galaxies in the observable universe. They've counted the galaxies in a particular region, and multiplied this up to estimate the number for the whole universe.