The use of steamships became very popular in the United States in the early 18oos after Robert Fulton had traveled to France and investigated what had been done there with the steam engine. In 1811, the first in a line of river steamboats left the dock in Pittsburgh to steam down the Ohio River to the Mississippi and on down to New Orleans, a major port of the United States. Steamboats were used on rivers and the great lakes for inexpensive transportation of goods. However, there were hazards and many ships were damaged in their excursions. Also, they burned wood and much deforestation took place during the era of steamboats.
A third advancement was in the construction of metal bridges which could sustain the weight of railroad cars, etc. Plans for such bridges such as the Manhattan Bridge date back to the early 1800s.
Another great boon to transportation was the creation of trains that could rapidly traverse the country with good. Later, with the invention of the refrigerator car, produce from California could arrive fresh in New England, for example. John Steinbeck's novel, East of Eden has a character who seeks to make money by transporting lettuce on the railways. However, his idea was premature because the refrigerator cars were not yet made.
I assume that you are talking about the United States. If so, here a few changes that happened in the early 1800s that helped make transportation easier.
First, there were more roads being built. The National Road is an example of one of these, but there were many more that were being built with private money.
Second, steamboats came into existence. These allowed travel against the stream of rivers.
Third, the Erie Canal was completed. This connected the Great Lakes (and thereby the Mississippi) to the East Coast.
A bit later (I'm not sure what counts as "early" 1800s, railroads started to boom. These were the ultimate transportation improvement.
Major developments took place during the late 1700's and early 1800's that laid the foundation of modern transportation system. The steam driven vehicles were developed in late 1700's. However, steam driven passenger cars were developed and first used in England in early 1800's. The first commercial steam steamboat service was first developed in the USA in 1807. The first stem locomotive was built in 1804. The firs successful steam railway began in England in 1825. Railway service in the USA was started in 1831. The railways played a major role in revolutionising the transportation system around the world.
Macadam system of surfacing roads, developed by John Loudon McAdam was also introduced in early 1800's in England. This system, which later spread around the world, made road travel much faster and comfortable.