In the picture below you can see what this joint is, technically those are a pair of articulated joints.

Misalignment in this important joint will inevitabley cause a bunch of issues in your body: from low backpain to neck pain and other problems. Because, if the base is not stable and symmetrical the whole building is at risk.

Many people have issues with it without knowing about it.

The best way to start is to consult the competent practicioner who could help with diagnose of dysfunction. For this purpose there usually are two tests: flexion test, stork test (Gillett test) etc. Googling that will help (“flexion test sij”, “stork test sij”). A pair of video examples of test by John Gibbons (video1, video2).  BTW, he is the guy who wrote one of Top 10 books from my list.

For those who want to read a bit more in-depth, I can recommend this article.
https://www.dailybandha.com/2015/06/the-sacroiliac-joint.html
And this blog is absolutley must-read for yoga lovers, and not for only them, though. Good portion of biomechanics.

Few excerpts from another article:

Research published in Clinical Biomechanics in 1989 determined that muscle balancing is key, and that in order to have optimal SIJ stability (and movement) you need to focus on what they called the powerful two – the gluteus maximus and biceps femoris – as they exert shear and torsion loads proportional to the strength of their contraction.

… researchers also determined that weakness in the posterior chain (glutes and hamstrings) and tight psoas muscles can lead to aberrant SIJ motion and loading. And, as with anything in the body, it isn’t always as simple as that, as the lats and connecting thoracolumbar fascia can also play a role in indirect stability to the SIJ.

This means that in order to correct a hypermobile SIJ, we need to focus on the surrounding muscles, especially those in the posterior chain, and correct any imbalances. Most commonly this means improving the strength of the gluteals, hamstrings and lats, but individual cases may vary.

Fixing a hypomobile SIJ can be a bit trickier, but believe it or not fixing muscle imbalances is exactly what we want to do in this situation, as well. We need everything to be working optimally around the joint to solve this problem.

To keep your SIJ functioning properly and pain free, you need to work on optimizing your posture, core stability, hip mobility and stability, along with strength and motor control. Even more, working on reciprocal movement patterns that challenge the core as well as work the contralateral lats and glutes is key here.

Four Exercises For Sacroiliac Joint

• Bear walk
• Glute bridge variations
• Plank variations
• Dead bugs