The Constitution is the Supreme law of the United States. When it went into effect, it didn't necessarily "change" any existing laws, other than replacing the previous Articles of Confederation. Note that the Constitution isn't a list of laws so much as it is the framework for the government.

This means existing laws remained in place. As long as they didn't conflict with the Constitution, there wouldn't be an issue. A law that did conflict with the Constitution would be challenged in court and found to be unconstitutional and therefore unenforceable.

Practically it did change things, since the Constitution called for a more centralized federal government versus the Articles of Confederation. An example of one of the changes was that prior to the Constitution, States each had the power to print their own currency. Under the Constitution, that power is reserved to the Federal government. So any State laws regarding the making of their individual currency became void since the States no longer had the power to do that.

Other powers changed as well - you had the creation of the bicameral legislature versus a single legislative body, and creation of the electoral college to elect the President - so states had to organize election laws and procedures to account for those sorts of things.

As for "British laws" - the majority of British statutory law basically stopped being in effect as soon as the States decided to be independent - at least major things like taxation - many states did continue to enforce or adopt or recognize British statutes that weren't in conflict with any new government. However, British common law was still the backbone of the American legal system. If you're not a lawyer, that's probably a confusing statement so let me break that down.

You have some laws that are statutory. So, for example, the legislature decides that theft is illegal and enacts a law against theft stating: "Anyone who intentionally takes the property of another without permission and with the intent to deprive the person of that property is guilty of theft."

Then you have common law. Common law, or case law, is based on the presedence of previous court cases. So here, you might have once upon a time person A brought an action against person B in court for taking his property without permission and the court found in favor of Person A. The next time that situation comes up, the court looks back at the prior decision and follows that decision. So you get this judicially created law against theft.

Typically in common law countries, there's a mix of the two. There's statutes enacted by the legislative branch and then interpreted by the judicial branch. So you get that statute against theft as written above, and then a court may decide how to define the word "intent" or "deprive" which further defines the law and becomes a binding precedent on future cases.

If you dig into the laws of different states, you'll find a lot that have a provision like this one in Florida's state constitution which says: "the common and statute laws of England which are of a general and not a local nature, with the exception hereinafter mentioned, down to the 4th day of July, 1776, are declared to be of force in this state provided the said statutes and common law be not inconsistent with the Constitution and laws of the United States and the acts of the Legislature of this state."

So what that means is, British common law and even some statutes remained in effect - to the extent that no state or federal law intervened. It's not uncommon for the United States Supreme Court even now to dig into some old British law texts to show the common law definition of a legal term. Blackstone's Commentaries on the Laws of England is still a fairly common reference in courts across the United States.

Because the federal and state governments continued to carry on the British common law tradition, there wasn't ever a time in limbo of "no laws" since a common law system allows a court to act even in absence of a statute on point.

I am not an historian, but in addition to what /u/Manofthedecade said above, also note that the Federal government was nowhere near as powerful regarding individuals as it later came to be. Initially Congress mostly passed laws relating to the structure of the federal government, trade, taxes and relations with the States. I got the sense your question was more along the lines of day-to-day laws?

Instead, states had all the day-to-day lawmaking power affecting individuals. To get a feel, you can skim the nature of the statutes passed by Congress in the first few Congresses: https://www.loc.gov/law/help/statutes-at-large/1st-congress.php . There also wasn't a clear feeling of what the Fed's powers were regarding citizens (instead of states).

When the federal bill of rights versus states' actions did come up in 1833 the Supreme Court said the federal bill of rights did -not- apply to actions by States, only actions by the federal government, see Barron v. Baltimore, 32 US 243 (1833) and read its short discussion. (most of the Bill of Rights today -do- apply to actions by states by a kind of backdoor approach through the Due Process parts of the 5th Amendment).

I do want to add a spin to /u/Manofthedecade 's response on, "This means existing laws remained in place. As long as they didn't conflict with the Constitution, there wouldn't be an issue. A law that did conflict with the Constitution would be challenged in court and found to be unconstitutional and therefore unenforceable. " Theoretically yes, practically no- the idea of the Supreme Court having the power to declare something unconstitutional is not in the Constitution. It was understood as a concept in state courts interpreting state constitutions, but it wasn't a 'thing' at the federal level until 1803 in Marbury v Madison, Chief Justice James Marshall held that that power was a direct implication of the Constitution's empowering the Supreme Court to adjudicate cases wherein a Federal law might conflict with a provision of the Constitution. Marshall was actually looking for the opportunity to do that, but it didn't exist before 1803. IIRC, the court didn't use that power again till Dred Scott in1857.

As far as a transition from Colony charters and law to State laws, it's a hodgepodge different in every state how much of their colony law they imported/ratified into the new State. It probably violates the AskHistorians rule, but you might take a look at Wikipedia to get a feel. Pick an original 13 colony and look at the entry on their Constitution or Code, in the history section. Or, if you really want to dive deep, there's a free source, The Federal and State Constitutions - Colonial Charters, and Other Organic Laws of the States, Territories, and Colonies now or heretofore forming the United States of America (1909) at https://oll.libertyfund.org/titles/thorpe-the-federal-and-state-constitutions-7-vols

Also, relating to the Common Law he mentions, yes it was very important, there was an extremely influential treatise in the Colonies called "A Commentary on the Laws of England," (often just called "Blackstone's Commentary" or just Blackstone's) which tried to compile the Common Law. It was published in the 1760's and was used a a strong authority by colony and later state courts in the absence of a clear statute or precedent. It was still a respected authority till the mid 1800's at least. If you have way too much time on your hands it's freely available on the web and in the Kindle store. I decided to try to get all the way through it once and failed at a mere 200 pages in.

And, that absence of clear precedent or statute happened very frequently. This absence was because precedents and even statutes were often not widely available- the collecting and widespread publishing of court decisions was a political patronage hit or miss affair until it started to standardize in the mid-1800s and really didn't take off till the 1870's. And, individual precedents actually at a granular level weren't given the level of respect they now have- a court would feel it was free to overrule a clear precedent if it conflicted with Blackstone. In fact, through the 1840's at least, newer 'case lawyers' (those who obsessively relied on precedents because of the better availability of cases) were held in a bit of contempt by older lawyers who instead reasoned from Common Law principles; they weren't good lawyers, they were mere bookworms.

Also also on the 'absence', states handled their laws much differently than they do today. There was no comprehensive one-stop where all the laws of say, Virginia, could be found, listed all nice and neat by subject. That didn't start happening till at least the 1810's and was very slow to take off. It wasn't finished in most of the states till the late 1800s. Instead they were a scattered list of individual statutes passed by the colony then state legislature over their entire existence, chronologically. If you were lucky you could find a set of books each with the laws by legislative session- e.g., "vol. 1, everything passed in 1776-7; vol. 2 everything in 1778-9, etc. Finding 'every' law by subject in a state would be a big chore- but for day to day criminal and civil stuff the lawyers and judges would know from experience and Common Law what the sense was.

A good source for this is the early chapters of The Invention of Legal Research by Joseph Gerken- it's pricey, but his initial paper is at https://works.bepress.com/aallcallforpapers/76/ EDIT: Also look at his page 78 (82 in the pdf) for a discussion of the idea of how precedence and Stare Decisis were thought of)