A counted cross-stitch chart is a grid. Each square is one stitch on the fabric, and the symbol or colour in the square says which thread to use. Empty squares are bare fabric.
The legend
Under or beside the chart is a table matching every symbol to a thread number and name, usually DMC. The charts on this site also list how many stitches each colour has, so you know which colours are a few accents and which are the bulk of the work. The thread colour database shows an approximate swatch for each number.
Grid lines
Every tenth line is drawn heavier. Counting in blocks of ten is far quicker than counting single squares, and the heavy lines line up with the tens on your fabric once you have stitched the first block. Most stitchers also mark the centre lines with an arrow; the charts here are centred on the canvas so the middle row and column are easy to find.
Where to start
Find the centre of the fabric by folding it in half both ways and creasing lightly. Find the centre of the chart. Start there and work outward. Starting in the middle means the design always ends up centred, whatever the fabric size.
Some people prefer to start at the top-left corner of the design, counting in from a fabric margin. That works if you have measured the margin carefully; the chart size calculator gives the finished size so you can position it.
Direction of the crosses
Each stitch is two diagonal half-stitches. All the top halves should slope the same way across the whole piece, or the light catches the threads differently and the finished piece looks patchy. Pick a direction on the first stitch and keep it.
Rows and blocks
Work one colour at a time within a small area, say a 10 by 10 block, then move on. Long jumps of thread across the back show through light fabric and waste floss. If a colour has many small scattered stitches (the verifier calls these confetti and limits them), do them last so you can see exactly where they sit.