how to use "each of the at least..."?

They("each of the" and "at least") are not one phrase. They relate to different parts of your example. So, there is no general meaning for "each of the at least".

But to explain the meaning of your example. You could also write it as: "each of the fiber fluid transmissive component cross-sections, which have at least one three-dimensional bond"

I'm a patent drafter and translator, and this sounds to me like a slightly clunkily written description or claim in a patent application (which is par the course in patent texts).

If one removes 'each of' for a moment, without additional context I would understand 'the at least one three-dimensional bonded fiber fluid transmissive component cross-sections' as meaning: 'the at least one cross-section of a component which is three-dimensional, bonded, and transmits fibre fluid'. ('three-dimensional', 'bonded', and 'fiber-fluid-transmissive' are each adjectives describing the component. Grouping the adjectives like this is common and clear to understand in languages like German, but is harder to understand in English. It is possible this text was either written by Germans or translated from German into English).

To answer your question, 'the at least one cross-section' is an accepted phrase in patent texts, and means that earlier in the text it has been explained that there is either one cross-section or multiple cross-sections. This means that, in each instance the text subsequently refers to the cross-section(s), it must be referred to as 'the at least one cross-section'. However, putting 'each of' in front of 'the at least one' makes the grammar a bit iffy in English to say the least. 'Each of the at least one' essentially means that, whatever the rest of the sentence says, it applies to each cross-section (whether there is one cross-section or multiple cross-sections).

A clearer way for the sentence to be phrased, depending on how it continues, might be: "the at least one cross-section of a three-dimensional bonded component that transmits fiber fluid is in each case..." OR "the cross-section(s) of a three-dimensional bonded component that transmits fiber fluid is/are in each case" (while this is perhaps clearer, patent texts usually avoid structures like this)

Unfortunately, patent texts like this are often challenging to understand for anyone who doesn't work with patents every day! Rules of grammar and clarity often regrettably fall out of the window!

p.s. I did a Google Search and found the original text this phrase appears to be lifted from: https://patents.google.com/patent/US20060163152. It is indeed a patent text and, based on the names of the inventors, appears to be drafted by Germans! Looking over the description appears to back up my explanation above.