The interstates were not the first superhighways; by the time a nationwide system was under construction, superhighways in many urban areas had been in use for 30 years. Even in rural areas, several divided, grade-separated sections had been built as interim improvements on many cross-country routes. When the 1956 highway act finally funded construction of the Interstate System (which Congress had technically created a decade earlier), about 1.5 percent of "federal-aid" and toll highway mileage was already to superhighway standard; today—though the statistics are not strictly comparable—about 19 percent is.
The concept of a limited-access, grade-separated, multilane facility was demonstrated in the 1930s with short urban stretches in and near New York City and Chicago's Lake Shore Drive. Several similar facilities were in place around the country by 1940, when the Pennsylvania Turnpike demonstrated the demand for cross-country superhighways as well. World War II slowed building quite a bit, except for projects like the Willow Run Expressway near Detroit that were useful for new defense plants.
After the war, the states and big cities were anxious to get their planned superhighways under way. Cities like New York, Chicago, and LA cobbled together what state and local funding they could assemble to begin construction of projects like Chicago’s Congress Superhighway, or LA's Hollywood and Long Beach Freeways. Looking to the Pennsylvania Turnpike as an example, many states turned to toll financing for corridors where traffic projections were high enough, resulting in the turnpikes of the Eastern Seaboard and industrial Midwest. Nearly all of these got Interstate numbers and became part of the network.
As for what the highway network looked like in 1955, after decades of slow but steady improvement, it was mostly (but not entirely) paved, and most U.S. highways were two-lane roads with shoulders. Lane widths were often only nine feet, though, not the 11-14 feet typical today on high-traffic two-lane highways. Some had three-lane sections, with “suicide lanes” in the center for passing. Many geometric aspects—sightlines, guardrails, median protection, intersections—were quite substandard compared to today. Most state highway systems were similar but even less developed; several states had stretches of unpaved roads on their state networks well into the 1960s.
I like Earl Swift’s The Big Roads as the most readable history of the Interstates, but Mark Rose's Interstate: Express Highway Politics 1939-1989 is the more scholarly source on the congressional machinations that led to the 1956 law.
In North America, the task of keeping out of the ditch or swamp was more important early on than the task of avoiding other vehicles. The definitive reference work on this subject is Peter Kincaid's 1986 book The Rule of the Road: An International Guide to History and Practice.
Writes Kincaid: "In summary, different types of transport, all used by right-handed people, tended to produce different rules of the road. Armed walkers and armed horsemen tended to keep left to leave their swordarms free. Horse riders kept left in any case because they mounted from the left and stayed near the edge where it was easier and safer to mount and dismount than in the middle of the road. People leading horses with their right hands tended to keep right because the led horse was then protected from passing traffic. Carters tended to keep right because they walked on the left side of their horses, leading with the right hand, and by keeping right could walk in the middle of the road...to avoid collisions. Postilion riders tended to keep right because they sat on the left-rear horse and thus could better judge clearances....Drivers who sat on the vehicle kept left because they sat on the right to keep their whip hands free and could judge clearances better when passing if they kept left." Kincaid describes other contributing factors such as conformance with neighbors (undoubtedly the reason for Canada), influence of colonization, national unity, imported vehicles, etc. Although we tend to think of a keep-left rule requiring right-hand controls, and vice versa, he points out a number of instances where curbside controls have been preferred to centerline controls.
As of 1986, he counted 118 "independent territories" with right-hand traffic and 51 with left-hand, adding: "The above figures show what a minority rule left-hand traffic is today. Countries which use it account for only about a third of the world's population, a sixth of its area, a quarter of its roads, and a sixth of its motor vehicles." A number of countries have changed their rule of the road, including, since 1950: Cameroon, Belize, Ethiopia, Sweden, Bahrain, Iceland, Burma, Sierra Leone, Nigeria, Ghana, and South Yemen. All these but Burma changed from left to right.
The American expert on this subject is Richard H. Hopper, whose article "Left-Right: Why Driving Rules Differ," appeared in Transportation Quarterly 36 (1982), pp. 541-548.