The most important thing in intarsia is to twist your yarns on the back correctly. Hold the one you're stopping over to the left and bring the new one up from under it. This will twist them automatically without a lot of hassle.
To start a new strand, you can knot if you want, or if I can explain it, I'll tell you what I do.
I knit the first stitch with the new color, leaving a tail to weave in later. Then I bring the old color strand across to the left on top of the new yarn and knit the second stitch with the new color. This twists them as you would as you were working along. That wasn't so hard to explain as I thought.
You do get a small vertical line along the back edges of a motif from bringing the new color up. It's really unavoidable. Inside a sweater, nobody will every know.
For small gaps in the pattern, if it's a one-time thing, you can strand and catch the yarn. If it's going to last for a few rows, your best bet is to start yet another new strand. It's a bit of a pain to have so many strands on the back, but if you carry the yarn across a small gap for several rows, that line of stitches will be thicker than the rest and tend to look puckered, even if your tension is loose.
Hope all this helps!