I use tailors basting but while I run my basting vertically on the fabric peices I don't bother keeping exactly to the grain line. Tailors basting involves taking short crossgrain stitchs about 1" apart vertically so you end up with long diagonal 'floats' and the fabric won't slip in either direction (if you just do a running stitch the fabric can slip in the stitiching direction).
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Sewing Techniques and Tips >> handbasting underlining to fabric