A lot depends on the degree of constipation you are experiencing.
If you are simply a few hours overdue and need to poop before going out or joining a group, then a suppository should get things moving fairly quickly. Five to ten cc's of liquid glycerin will empty the rectal vault in less than five minutes. If you do not have liquid glycerin, then try a glycerin suppository.
If you are experiencing recurring flatulence and speed is of the essence, then a sodium phosphate enema (about 4 ounces) held for five to ten minutes will evacuate the rectum and sigmoid. That usually flushes the gas along with the stool and leaves you good to go for about eight hours.
If you sense the stool is hard and/or larger in diameter than normal, a mineral oil enema is typically helpful. You need about 4 ounces of mineral oil. That size is sold by Fleet in a squeeze bottle. Once in, remain laying down for an hour. Often in that hour you will feel something like marbles moving around, which is a cue to take a seat on the toilet. Often hard stools are formed of small stool clumps and the mineral oils separates the clumps. (See the Bristol Stool Chart at https://upload.wikimedia.org/wikipedia/commons/3/31/Bristol_stool_scale_neutral.png) Mineral oil is quite useful when dealing with stool like item 2 in the chart. Also wear absorbent disposable underwear such as Depend or Always briefs for one to two days afterward, as residual oil in the rectum will leak when least expected. Nothing will get you pariah status faster than leaving an oil stain on office chairs.
This will get a lot of pushback, but if traveling over road for long distances, I use a 1.5 to 2 liter tapwater enema about two hours before departing. This usually flushes part of the transverse colon, empties the descending and sigmoid colons and rectum. This usually allows two days of travel without concern of having to use toilet facilities of unknown condition. If you carry disposable bags while traveling, buy bottled water for use as the enema solution. You do not know the source or quality of tapwater in many locations.