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Hi Terrie, Welcome to the Quiltingboard. I looked at the link you were inspired by and agree with JenniePenny. You note you have made your half square triangles. I expect that to mean you have made your half square triangle 'blocks'.
If you are asking what to do next: you will lay the blocks out to form the pattern you want in the quilt top. It sounds as if you have done that.
Next you will seam all the blocks in column 1 into a strip. Do so with all your columns. I work in columns (top to bottom). You mention sewing the blocks into rows (left to right) and that would work just fine to.
Once you have sewn your strips, lay them out again to be sure you kept the pattern you want in your quilt top. If it looks like you want it to then you are ready to seam column (or row) 1 to column (or row) 2. Press your seam. Seam column (or row) 3 to column 2. Press your seam. Keep adding strips until you have completed the quilt top.
I am making my 2nd Bargello. Instructions say to start stitching the seam on the fist column at the top, start stitching the seam on the second coulmn from the bottom, the 3rd column from the top, the 4th column from the bottom, etc. This helps prevent the waving motion we sometimes see in our seams as the quilt top is coming together.
Quilting the top means putting down the backing, batting in the middle and quilt top on the top creating a 'sandwich'. When quilting the sandwich it is recommended to start in the center and quilt out.
I hope we addressed your question. If we did not please let us know.