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Hi there,
Weaving in the ends can be done in various ways. Basically what you do is getting the tail of the yarn that's left after tying a knot to go through the back of the stitches. I use a crochet hook but you can also use a yarn needle.
There are two simple, common ways to do it, one is by working along one row of stitches and let your tail go through one stitch, skip the next two or three and let your yarn go through the next one again and so on.
The other is by doing some zig-zagging through more rows of stitches.

If you don't get it, I found these two videos on Youtube that might be useful for you:
Weaving in ends on stockinette stitch.
Weaving in ends on ribbing.

After you have weaved in the ends, do you just cut off the rest of the tail?

I'm always worried that if I leave the ends loose it may unravel, therefore after weaving in the ends I tie a knot redface


I was also wondering when sewing knit pieces together (ie. in the case of pockets or if the project has pleats etc.), do you use the same technique to attach the yarn (ie.weave in the ends) when it requires that you use a new piece of yarn?