What is a grade?

A grade is a measure of the contrast of a print. The higher it is, the more contrast the print will have.

Contrast curves for Ilford Multigrade RC Deluxe and Portfolio papers:

As you can see from the curves above, the higher the grade, the faster the density* increases.
*More density =more black.

In practical terms, with a grade 3 filter, the deepest black will be reached twice as fast as with a grade 0 filter [1].
The brightest areas of the print, however, are only slightly affected by a change in grade.

To simplify:

Increasing the grade means darkening a print without significantly affecting the brightest areas.

How to find the right grade?

There is a simple method to find the grade that best suits your print. I didn’t invent it, but found it here: https://www.youtube.com/watch?v=woXZb8gjG4o&t=1s

This method can be summarized as follows:

Find the blacks and whites you like best, then make them appear at the same time by choosing the right grade.

A practical example

Test strip at grade 2

First, make a test strip at grade 2 (standard).

Here, the blacks appear too early. We want to delay them so they coincide with the whites we like.
To delay the blacks, we choose a lower grade. In this case, I decided to go straight to the lowest grade (0).

Test strip with a more appropriate grade

Now make another test strip. If the desired blacks and whites fall at the same point, you can stop: you’ve found the right grade and exposure time.

Otherwise, repeat the previous step.

Don’t stop there

And there you go-you’ve found the overall contrast.
That doesn’t mean there’s nothing left to do. In most cases, you’ll want to use dodging and burning to achieve the best result.

Here, dodging/burning would help bring out the snowdrops in the grass.

[1] Approximation, just to give an idea.