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Crochet motifs (or crocheted squares) can be joined to each other in one of the classical ways, shown below. There are no "correct" or "incorrect" ways for joining motifs together. It is only matter of your preferences. Try them all and choose the one you are comfortable with the most.
Motifs can be joined by a crochet hook. This method has more technological flexibility and decoration features than joining motifs with a yarn needle. You can use slip stitch, single crochet or chains to join elements to each other. Two motifs can be placed right side-to-right side or back side-to-back side. Decorative effect will be different.
This is the easiest method of joining motifs. Hold two motifs together (right sides facing each other). Using a yarn needle and matching color and thickness thread sew motifs together through the back loops only. (A new window opens for your reference.)
Motifs can be joined by a crochet hook. This method has more technological flexibility and decoration features than joining motifs with a yarn needle. You can use slip stitch, single crochet or chains, to join elements to each other. Two motifs can be placed right side-to-right side or back side-to-back side. Decorative effect will be different.
Connect motifs while crocheting their last row. Method works the best if motifs have arches on the outside edges. This way connection will look the most decorative and the least noticeable. Here is a good example where this method to join crochet motifs (or squares) will work perfect. I used it for crocheting a lacy crochet shawl many years ago.
All methods of joining crocheted elements, mentioned above, will work if elements create a regular repeating pattern. When won't they work for joining motifs? Two cases at least can be mentioned here.
Let's consider joining of motifs #2 from Irish Crochet page. 8 petals allow to join 4 more motifs around each motif. We will sew 4 motifs together(or better use "join-as-you-go" method). As a result, in center we have a pretty large empty space. To fill it, we usually use an additional small motif-insert. It looks more natural if the inserting element is a fragment of a major motif.
Sometimes motifs, which have to be joined to each other are the elements of the pretty complicated composition (like in Irish crochet laces). None of the methods presented above will work. The joining requires some special techniques. Usually motifs are inserted in some background. In most cases, this kind of joining crocheted elements looks almost like a "rocket science" even for the pretty experienced crocheters.-:)
There is a very good saying :"Our eyes are afraid, but hands just do it!" You can try one of these methods on your own together with me. I have never tried to do it before. Here is a link to follow: Motif Pattern page.