Stone fruits start to soften slightly and usually become easier to pull off the stem when ripe. Any remaining background color typically changes from greenish to yellowish. Some varieties are quite forgiving; they hold their tree-ripe quality for several days or more. Individual fruits of other varieties may have a single best day for picking.
Judging ripeness is mostly a matter of experience, learning by doing. By trial and error you learn whether you prefer a particular fruit on the firm side or more ripe, and when to pick it. Learning how to pick each variety at its best is part of the fun of home fruit growing.