Measure once, measure twice, then cut. This is the most important tip, unless you want to buy more fabric.
Invest in sharp scissors - they don't have to be dressmaker's scissors, but sharp is essential.
Iron up hems before sewing - sometimes you can avoid having to pin and tack if you do this - and the resulting finish is neater.
On a similar note - press the finished garment with a damp cloth between the iron and the fabric - unless it's velvet! Steam, don't press velvet.
If you're in a hurry, and don't want to tack seams, pin using pins which are at right angles to the direction of sewing and sew straight over them. Note: one day, you will get a broken needle when it hits the pin square in the middle, and doesn't slide off, but it's only happened to me twice in forty years of sewing.
It's quicker and neater to line a sleeveless top or bodice than it is to use facings.
If you're sewing fine fabrics, use a strip of Stitch & Tear between the layers of fabric to minimise pulling and gathering.
Always use a ball-point needle when machine sewing synthetics - it slides around the threads in the weave rather than trying to cut them.
Don't wait for your needle to break before changing it - they do wear!
Know your machine, look after it, clean it, oil it and it will last for years.