Decade - 1940s

Assuming you're referring to US money, the denominations would be familiar today. Some of the designs would too, but not all. Specifically:

Lincoln cents were the most common penny, although occasionally an Indian head cent might pop up in change. All Lincoln cents were "wheat" cents - they had the words ONE CENT surrounded by two wheat ears on the back. The only change happened in 1943 when cents were made of zinc-coated steel due to wartime copper shortages.

Jefferson nickels had been introduced in 1938 and carried the same design as those used till 2003. A lot of buffalo nickels were still in use though. During WWII, Jefferson nickels were struck in a silver alloy to save nickel for the war. The design was basically the same except the mint mark was a large letter above the dome of Monticello.

Dimes had the famous "Mercury" design. It was actually Miss Liberty wearing a winged freedom cap, but it looked so much like the Greek god Mercury that everyone called them Mercury dimes. These coins were made of 90% silver and 10% copper.

Quarters had the same design that was used till 1998 - Washington was on the front and a spread-winged eagle was on the back. Once in a while an old Liberty Standing quarter could be found, too. Like dimes these coins were 90% silver.

Half dollars were very common in circulation. Till 1947 they carried the beautiful and famous "Walking Liberty" design on the front and a perched eagle on the back. In 1948 a new design came out, featuring Benjamin Franklin on the front and the Liberty Bell on the back. All halves were also 90% silver.

If you were in the west, you might get a silver dollar in change. Most of them were Peace dollars, struck from 1921 to 1935 to commemorate the end of WWI. They had a picture of Miss Liberty on the front, and an eagle and the word PEACE on the back.

All $1 bills were silver certificates. These bills were backed $1 to $1 with silver on deposit with the Treasury. They looked a lot like modern $1 bills but had blue seals and serial numbers instead of green. During WWII special brown-ink bills were printed for use in Hawaii. They could be easily identified and declared worthless if captured by the Japanese.

$2 bills weren't used a lot but were more common than today. These were all United States Notes which were printed with red ink. They had the same front design as today, but the back was a picture of Jefferson's home Monticello.

$5 bills were issued as silver certificates (blue), US Notes (red), and Federal Reserve Notes (green). The front had a small picture of Lincoln in an oval, and the back had the Lincoln Memorial similar to today's bills. Like $1 bills, special brown ones were printed during WWII.

$10 bills were issued as silver certificates (blue) and Federal Reserve Notes (green). Hamilton's picture was small and in an oval like Lincoln's. The back had a picture of the Treasury Building, but it was part of a street scene instead of a full-front image. Again, brown ones were printed during WWII.

$20 bills were issued as Federal Reserve Notes. Jackson's picture was small and in an oval like other bills. These too were issued with brown ink during WWII.

$50 and $100 bills followed the same pattern, with pictures of Grant and Franklin shown in small ovals in the center of the bills' fronts.

If you were quite wealthy, you could also get a $500 billwith a picture of President McKinley on the front and the words FIVE HUNDRED DOLLARS on the back, or a $1000 bill with a picture of President Cleveland. There were even $5000 and $10000 bills but very few people were rich enough to have them.