Short Answer

Four suggested resources:

1. Up from Slavery, a book by Booker T. Washington;
2. Research information on Juneteenth (I agree with T.E.D. on that!);
3. The Emancipation Digital Classroom in the Civil War Research Engine at Dickinson College, Pennsylvania;
4. Browse through the Slave Narratives on the University of North Carolina's web site. (Note: alternative to gutenberg.org - UNC has same content as shoover's suggestion.)

Among these resources you will find detailed answers to all four of your key questions:

How did they learn of the proclamation or the abolition? What did they say and do? What did his/her master say and do? How did they transition to freedom?

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More Information on These Four Suggested Resources

1. Up from Slavery

According to the Wikipedia abstract on Up from Slavery, it is:

the 1901 autobiography of American educator Booker T. Washington (1856-1915). The book describes his personal experience of having to work to rise up from the position of a slave child during the Civil War, to the difficulties and obstacles he overcame to get an education at the new Hampton Institute, to his work establishing vocational schools—most notably the Tuskegee Institute in Alabama—to help black people and other disadvantaged minorities learn useful, marketable skills and work to pull themselves, as a race, up by the bootstraps.

Here is a relevant quote from Washington's Up from Slavery as found on Wiki's Slavery in the United States - The end of slavery topic:

Booker T. Washington remembered Emancipation Day in early 1863, when he was a boy of nine in Virginia:

As the great day drew nearer, there was more singing in the slave quarters than usual. It was bolder, had more ring, and lasted later into the night. Most of the verses of the plantation songs had some reference to freedom.... Some man who seemed to be a stranger (a United States officer, I presume) made a little speech and then read a rather long paper—the Emancipation Proclamation, I think. After the reading we were told that we were all free, and could go when and where we pleased. My mother, who was standing by my side, leaned over and kissed her children, while tears of joy ran down her cheeks. She explained to us what it all meant, that this was the day for which she had been so long praying, but fearing that she would never live to see. [emphasis added]

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2. Juneteenth

Wikipedia describes Juneteenth as:

... an American holiday that commemorates the June 19, 1865, announcement of the abolition of slavery in the U.S. state of Texas, and more generally the emancipation of enslaved African-Americans throughout the former Confederacy of the southern United States. Its name is a portmanteau of "June" and "nineteenth", the date of its celebration. Juneteenth is recognized as a state holiday or special day of observance in forty-five states.

From the History section of Wiki's Juneteenth entry, this information is found:

On June 18, Union Army General Gordon Granger arrived at Galveston Island with 2,000 federal troops to occupy Texas on behalf of the federal government. The following day, standing on the balcony of Galveston's Ashton Villa, Granger read aloud the contents of "General Order No. 3", announcing the total emancipation of those held as slaves:

The people of Texas are informed that, in accordance with a proclamation from the Executive of the United States, all slaves are free. This involves an absolute equality of personal rights and rights of property between former masters and slaves, and the connection heretofore existing between them becomes that between employer and hired labor. The freedmen are advised to remain quietly at their present homes and work for wages. They are informed that they will not be allowed to collect at military posts and that they will not be supported in idleness either there or elsewhere.

Formerly enslaved people in Galveston rejoiced in the streets after the announcement, although in the years afterward many struggled to work through the changes against resistance of whites. The following year, freedmen organized the first of what became the annual celebration of Juneteenth in Texas.

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3. The Emancipation Digital Classroom

Here are some examples to be found there, each of these from a different and interesting perspective:

Thomas Rutling Recalls His Freedom;
... (from a freed slave's perspective)
Union Recruiting Agent Spreads the "Good News";
... (from an emancipating Union officer's perspective)
Young Planter Witnesses Black Freedom.
... (from a plantation / slave owner's son's perspective)

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4. The Slave Narratives

All of the Narratives are stored online this website in HTML and XML format. There are hundreds available. Start in the section from about 1865 onward. I found this title which has some interesting personal memoirs of emancipation: Fifty Years of Slavery in the United States of America by Harry B. Smith, in the 1890-1899 section. Here is a quote from Chapter 7, pp 122-124 (this quote is presented verbatim as written by the author, himself a former slave - if you are looking for authentic personal accounts from those who lived it, in their own words, here is one of many found in the Slave Narratives):

There was great excitement and amusing scenes occured when the slaves on Hay's plantation heard the news of Lincoln's emancipation proclamation.

Some days had elapsed after the freedom of the slaves, when a number of Union men were passing, enquired of the slaves if their master had set them free. Massa Hays began to be alarmed for fear of being arrested, in case he did not inform them of their freedom. One morning as the slaves were eating. Massa Hays came in an walked around the table very uneasy, and bracing himself up in the best manner possible, spoke to them in this manner, "Men and women hear me, I am about to tell you something I never expected to be obliged to tell you in my life, it is this: it becomes my duty to inform you, one and all, woman, men and children, belonging to me, you are free to go where you please." At the same time cursing Lincoln and exclaiming, if he was here, I would kill him for taking all you negroes away from me.

After old Massa had cooled off from this painful duty, he told them to go to the grocery where he had whiskey barreled up and help themselves and get what they wanted. Then commenced a great jubilee among, not only the slaves, but old Massa, and all on the plantation seemed to join in the festivities. Old Massa got drunk and repaired to his room. His daughter, a fine young lady never known to drink, was much the worse for drinking. All were cheering Abraham Lincoln, while old Massa was too drunk to notice much. Old Aunt Bess an old colored woman, and very religious, who looked after the children, as well as the rest, used too much wine and to show her mode of rejoicing, sang old time songs, which added very much to the celebration. Preparations were made and at night dancing was began in earnest, and kept up until morning. Old Massa giving all liberty to help themselves to everything. Some of the slaves did not fully comprehend what it all meant, while others, more intelligent, enjoyed it to the full extent. Never was such a scene witnessed on the plantation before.

The writer cannot picture it to the reader, the rejoicing on this plantation and other places in the vicinity, on the announcement of the freedom of the slaves. Old Aunt Bess exclaimed, "bress de Lord, Im glad de Lord has spared me to see dis great day, my children are all free," she singing and shouting all the time.

Knowing what a great day this was to the enslaved negro, it is truly no wonder to the intelligent reader that they rejoiced and still keep in memory the emancipation day and will for all future time to come. History will repeat itself, and in ages to come, President Lincoln and many of the brave men will be immortalized.