Some manufactured centre finders are a bit slow to use on a batch of items and need accurately squared timber. The type with a blade to indent cross lines on spindle ends can easily start splits in the wood.
The finder I use most often is simply a small wooden block, with a hole drilled to be a push fit for a short bit of pencil. The hole is off centre, a different distance from each of the four sides of the block, so by turning it on different sides there is some height adjustment. Put the spindle blank and the pencil block side by side on a flat surface and mark a line across the end of the blank. Flip the blank 90 degrees and repeat so that all four sides are done. The result is a small square marked on the end of the blank, from which the true centre can be found by eye easily enough. This is not super-accurate, but good enough for most purposes, and it is quick. I have several pencil blocks in different sizes so I can pick the one most suited to the size of the spindle blank. The blank does not have to be square and the pencil block can mark cylinders equally well. A nail through the block can be used instead of a pencil.
When part of the spindle is to remain square after turning, you need a more accurate centre For this I made a cylindrical wooden insert for a four jaw chuck. I use engineering type jaws in my chuck, but any self centring chuck should work. The insert is a sliding fit in the body of the chuck and has a steel point inserted. The centre mark left in the insert after turning it gives the location for the point. To use the finder, put the chuck with insert on the bench, adjust the jaws to be a sliding fit on the blank, insert the end of the blank and give it a tap. The steel point marks the centre nicely. A batch of same-size blanks can be done in no time. The blank has to be accurately square to use this method.