Beginning on the cantankerous printing presses in Southwest Washington and moving on to a central warehouse in Kansas City, America's new 22-cent stamp finally began appearing this week in post offices and vending machines and on envelopes across the country.

The stamp had a long and somewhat tortuous arrival. Its saga began 21 months ago, when the U.S. Postal Service Board of Governors petitioned the Postal Rate Commission for a rate increase, initially seeking a new first-class rate of 23 cents. A year of fierce lobbying followed before the board finally settled on the 22-cent stamp in mid-December.

Even then, the trip wasn't completely smooth. Last week, the big "C" press at the Bureau of Engraving and Printing collapsed, sputtering to a stop in the middle of its press run of stamps.

That didn't stop the Postal Service. The print run was switched to a backup printing press. And until enough new 22-cent stamps have been printed, the agency will fill in with its stock of non-denominational "D" stamps and a supply of 2-cent stamps to go along with the outdated 20-cent ones.

The alphabet stamps are printed in advance and kept on hand for shortfalls such as the ones that occur when a new rate increase takes effect. Since they bear no price, the Postal Service can charge whatever it needs to for them. However, the stamps can be used only on domestic mail.

The agency already had about a billion of the "D" stamps on hand when the rate increase was approved. Once they are used up, the Postal Service will print a new batch of "E" stamps, which will be left in storage until the next shortfall.

By March 29, according to Postal Service spokesman Bob Hoobing, the official 22-cent stamp, emblazoned with an American flag, will have made its way into every post office in the country, retiring the "D" stamp.

The rate changes will add more than $2 billion a year to the Postal Service's coffers, in part to help defray the costs of a new labor contract, estimated to be an additional $1.3 billion a year by 1986. The costs of changing rates -- printing costs, mostly -- are usually recouped in the first few weeks of a rate change, postal officials said.

It takes about 120 days to implement a rate change, according to postal veterans who have seen nine rate increases -- totaling 633 percent -- since 1958, when the price of a first-class stamp rose from three cents to four. Most of the time is required to produce the sheer volume of stamps -- 6 billion of them -- that are printed on one of the Bureau of Engraving and Printing's five presses, running 24 hours a day, seven days a week.

The process this year was more complicated because "the domestic rate and international rates are changing all at the same time," said Jim Van Loozen, Postal Service manager of customer relations. The basic international airmail rate for a half-ounce letter increased to 44 cents this week. A postcard will cost 14 cents.

The Postal Service prints about 30 billion stamps a year, a volume that won't drop with the price rise. About a third of the items the agency handles bear a stamp.

For postage-meter users -- which includes an increasing number of federal agencies -- the changeover is as simple as moving a dial. Meanwhile, in post offices around the country, employes are trying to memorize new rate tables.

And in Southwest Washington, on the banks of the Potomac, the presses are still rolling off sheets of flag stamps. Said Van Loozen: "I know they're printing like crazy down there."