The join-as-you-go method of joining granny squares is my go-to method of joining. In essence, you work the final round of the granny square and join to the adjacent square with a slip stitch at corresponding points. In the example below I have done this all with a single joining colour, but the method also works when joining each square using a different colour for the final round for each square – you can see an example where I did this here.
Abbreviations/Crochet terminology:
UK terms are used throughout.
Ss – slip stitch
Tr – treble crochet
Ch – chain
Method:
Fig 1. Take the first square (purple) and complete the whole round in the joining colour Fig 2. Take the second (yellow) square and complete one side in the joining colour

Fig 5. SS into corner space of square above (purple) Fig 6. 3tr into corner space of yellow square
Fig 7. summary of how to work the join at the corner
Fig 8. continue working along with 3tr in the yellow square and ss into the purple square between the treble clusters Fig 9. In the corner work 3tr in yellow square corner and then ss into purple square Fig 10. Work 3tr in the yellow square corner and then continue with 3tr in spaces along side Fig 11. complete the round
Fig 12. Continue to add squares so that you have a strip Fig 13. Adding a second strip – work 2 sides of green square, join to the purple square on the third side Fig 14. When reaching the corner, work 3tr in the green square’s corner space Fig 15. SS into the corner of DIAGONAL square (yellow) Fig 16. 3tr in the corner of the green square Fig 17. Complete the round on the green square
Fig 18. The next square added (Purple#2) will join to two other squares Fig 19. Work along one side of Purple#2
Fig 20. Join with a SS to green square Fig 21. Work along the Purple#2 square whilst slip stitching into the green square Fig 22. Needle indicates where to work the slip stitch, which is into the DIAGONAL square (the first Purple square in this case)
Fig 23. Continue working back down Purple#2, now slip stitching to the yellow square Fig 24. At the corner add the SS into the DIAGONAL square (Grey) Fig 25. Needle indicates position of the SS Fig 26. Complete the square
Continue adding strips of squares