Karyotyping should be done during the metaphase cycle, when the chromosomes are distinct and easily counted. To obtain a sample with a good number of cells in metaphase, typically blood or skin cells are collected. Some drugs are used to stimulate division and lock cells into metaphase: see Preparing a Karyotype.
Another procedure done here: Karyotyping X. tropicalis to karyotype a species of frog, simply stains cells in the tadpoles, which are already actively dividing.