The removal of the crown from the stem should be simple. Carefully grip stem with vice or pliers were it will not get damaged with some tape around to protect it and wind the crown anti-clockwise. You might need another set of grips if this is very tight.
A few additional points if I may. Stem damage and the resulting damage to the stem bearing hole in the mainplate and/or barrel bridge is a very common issue to encounter- and it all stems (ha) from improper handling of the stem when changing a crown. Creating burrs on the hub of the stem or any other component must be avoided at all costs, as this is what will act as a reamer on the mainplate during use. Needle-nose pliers can be used on the excess threads (if they are present) or on the winding hub, as long as they are not too wide and bear on other surfaces of the stem. Alternatively, a good quality pin vise with a square hole can be tightened onto the square of the stem, if the detent slot shoulder is thick enough to handle the torque (a judgment call based on the size of the stem).
In the 6309 diver's 2-piece stem system, however, things are a little different. The male stem portion that screws into the crown can be carefully held on the two flats near the end to remove the crown. Loc-tite is most often used on crowns to make sure they do not loosen over time- many times heat is needed to release the loc-tite so that the crown can be removed. Heat from a lighter might be enough, sometimes a small butane torch is necessary though.
Check new crown winds on fully and fits in watch and hands move and day/date sets. Take out of watch then apply some glue on stem end and wind new crown and leave to set. If you have difficulty with day/date or time setting it will probably be to much stem wound into crown.
It is best to screw all crowns on as tight as possible, with the addition of loc-tite on the threads, as they undergo a lot of stresses in the course of use and can loosen if not absolutely tight. Always screw the crown on as far as it will go onto the stem. If problems in setting exist as Melt mentions, then it is necessary to replace the stem, cutting it a little longer than the too short one. In the case of the 6309 two-piece system, however, all lengths are predetermined by design, so sizing the stem by cutting threads is not possible nor necessary.