How we came to worship on Sunday

HOW THE SABBATH WAS CHANGED FROM SABBATH TO SUNDAY 
From a historical point of view, the change from Saturday to Sunday was a process, it wasn't something to happen overnight. Before we take a look at that process I want to express that Sunday worships started not because of a biblical command. It started because of prosecution of the early church by Pagan Imperial Rome, and you can take a look at this for yourself. This process was in three parts, 
(1) The early church kept Sunday because of prosecution, 
(2) Constantine Passes Sunday laws to Christianize his pagan empire because Christianity was growing stronger and taking over his land. 
(3) And the Catholic Church pass another Sunday law to strengthen Constantine Sunday laws because afterward, the early church was still keeping the Sabbath. 
But let's take a look at the process, detail. 
WHEN DID SUNDAY WORSHIP START. We have the process starting in 150 A.D. Why, because Justin Martyr records in the (Clark's Ante-Nicene Library, Chapter LXVII, p. 185, 1953 edition) the only authentic source where was the START OF THE CHANGE. The other sources like the Didache, or the Epistle of Barnabas, proven none authentic. Since Justin martyr has the only authentic source which is placed at 150 AD this means, it is the start of the process. Also, that proves the apostles and the early church kept the Sabbath not Sunday. 
So from 150 and on the church started to keep Sunday, but they didn't only keep Sunday they kept Saturday Holy also, this is recorded in (—Church History, Apostolic Age to A.D. 70, Section 29.). There were three groups of Christians at that time. (1) You had the Romans Christians who kept Sunday. (2) You had the Gentile Christians who kept both days. (3) And you had the Jewish Christians who kept Sabbath. So from 150 to 321 AD many wars between the Jews the Christians in the Roman empire. 
ENTER CONSTANTINE. Constantine saw this as a problem because he wanted to paganize his Roman Empire. Christianity was growing in his empire and it was starting to overthrow it, no matter how many prosecutions they did to it. So he passed into law in 321 AD for the first time, that they had to keep Sunday as a LAW or they will go to jail. Here is the law,❝On the venerable Day of the sun let the magistrates and people residing in cities rest, and let all workshops be closed. In the country, however, persons engaged in agriculture may freely and lawfully continue their pursuits: because it often happens that another Day is not so suitable for grain-sowing or for vine planting: lest by neglecting the proper moment for such operations the bounty of heaven should be lost.❞ 
(—ii. Philip Schaff, History of the Christian Church Volume 3 (Edinburgh: 1884): 380, note.) The early church, before this law didn't keep Sunday because it was a law or a command from the Bible, they kept it because of prosecution. The Jews and the Roman empire were at war a lot, and the early church since they kept the Sabbath, the Roman empire confuse them Jews and they were killing off the Christians thinking thus was Jews. So the EARLY CHURCH decided to keep Sunday, because of prosecution and wars, but from no a biblical command. 
There were Christians who kept Sunday but also they were Christians who were true to the word of God and they kept Sabbath, this is the remnant that was alive at that time. Papal Rome saw this as a problem so they passed into law or once again to strengthen Constantine's laws, that the early church had to stop keeping Sabbath and start keeping Sunday, we see this here; ❝Christians shall not Judaize and be idle on Saturday (Sabbath), but shall work on that Day: but the Lord’s Day, they shall especially honor; and as being Christians, shall, if possible, do no work on that day. If however, they are found Judaizing, they shall be shut out from Christ❞ 
(—Rev. Charles Joseph Hefele, Henry N. Oxenham (trans.), A History of the Church Councils from 326 to 429 Volume 2 (Edinburgh: T. and T. Clark, 1896): 316.) 
And this is how the change came it was a process that happens gradually over time. And this was so effective that now we see practically the whole Christian world keeping Sunday and Sabbath.