Slipping First Stitch

Many patterns say to slip first stich. I understand slipping stitch from left needle to right without knitting or purling but when I slip first stitch, it just sits there and actually can become separated from rest of stitches as they are worked. Is there a way to wrap stitch or what. How do you slip first stitch, be it either as purl or knit and get it to work?

If you slip the first stitch of one row, it’ll get knitted like a normal stitch when you go back across (because on the next row, it’s the last stitch). The result will be a stitch that’s somewhat stretched because it goes over two rows instead of one.

Thank you - appreciate your help.