Finding the centre in a blank is a regular exercise for most turners. There are turners out there who can do it by eye, and they won’t need this. Then there’s the method using a pencil and a steady hand, relying on keeping the same hand position. Works OK, but is not precise and can only be used on square blanks.
One can go and buy a cheap plastic one from Axminster (£4.20) or a proper engineering one (£8.00 and up). Or you can spend a few minutes and make yourself one like this:
It’s dead easy: From a piece of plywood (18mm in my case, by almost anything will do), cut a right angle of about 6″ in both directions (more if you can afford it), with about 1″ width of each arm (more for longer arms). The only really important thing here is to make sure the inside is as close to a right angle as you can get.
Then either re-use the remainder of this piece of ply, or find another piece and cut a triangle with the two short sides of about the same length as one of the arms, and a right angle between them. This guarantees that the long side is at a 45 degree angle to the short sides.
Clean up all cuts and glue them together, making sure that the triangle sits just slightly off from the inside corner, to allow for your pencil to get right into the corner. Once the glue is dry, this can be used to find the centre on square or round stock, up to a diameter that is roughly the length of the long side of the triangle (square root of twice the square of a short triangle side, or arm length, i.e. for a 6″ square this works out as 8.5″.