I start with new thread in one of two ways-
Loop method - when using an even number of threads I take a long strand double it over and thread the two loose ends. This leaves a loop at one end. Come up through the fabric from underneath go back down in the appropriate hole and thread the needle through the loop on the underside. A nice neat secure start.
Pinhead start - if I'm using an uneven number of threads, if the threads have already been used and cut or if I'm using varigated threads I will do a pinhead start. I read about this on one of the Ezboards (can't remember which one) and just love it.
It works best on linen because you need 9 holes.
1 2 3
4 5 6
7 8 9
Come up from underneath through hole six - make sure you keep hold of a wee bit of thread underneath.
Go back down through hole five.
Go back up through hole four - remember to hold that wee bit of thread tightly.
Go back down hole five.
Start your cross stitch by coming up through hole 7.
When the cross is made the small pinhead start will be covered and you will have a secure and neat start. Although it sounds fiddly I've become quite speedy at it. In fact because I don't have to flip the frame I can probably do it quicker than a loop start.
I'm not as happy with how I finish stitches. Where possible I thread under a few stitches on the reverse side do it again and then snip close to the base.
I believe it is possible to do a pinhead finsh - I need to research this a bit more 'cos I'm not sure how that would work. Surely you'll see the finish on top of the cross - unless of course you move the cross out of the way and will that effect the tension of the stitch.
Time for a bit of practice I think.