That's a VERY general question. Similar questions like yours have been asked and answered, so you should search around. You will probably get better answers by making a thread with something more specific. Is there something about the 300s you want to know about? Some profession, class, or type of person you are interested in?
The daily life of a farm slave would be very different from a teaching slave. A freedman working as a money lender would have a very different story than one overseeing a suburban villa. A gladiator's life would be different from a soldier, just as a consul would be different from an orator.
The 300s specifically were a time of instability in many areas of society. The Roman Empire was on the brink of collapse, and while your life might be very different depending where you lived, even in the East, where the Empire would fade into the Byzantine Empire, many things were up in the air.
You can see the instability clearly in the inflation of the denarius, a coin which was the most used form of currency. The silver content was diluted (debased) until there was practically none left, leaving the “silver” coins worthless. In 301, the price of a pound of gold was fixed at 50,000 denarii (already very high). Ten years later it was at 120,000. By Constantine’s death in 337, a pound of gold was worth 20,000,000 denarii. More on inflation here: http://wiki.mises.org/wiki/Money_and_banking_in_Ancient_Rome#Inflation_in_numbers
So I don’t know why you chose the 300s to ask your question, but there is a ton of difference between 301 and 399 AD. The life of any person might be very different for somebody of the same profession 10, 20, or 100 years later.
Also, it's much easier to get a sense of what daily life for male Roman Citizens living in the city than for any other class, so most answers will be about them. If you want to know about freemen/women, freedmen/women, slaves, women in general, children, temple workers, bankers, prostitutes, law makers, gladiators, soldiers, messengers, etc. those are all different questions.
Here's an answer about "daily life of a Roman boy": https://www.reddit.com/r/AskHistorians/comments/1ttn6d/what_was_life_like_for_a_boy_in_ancient_rome/
That mod, celebreth, also has many answers about "a day in the life" of Romans here: https://www.reddit.com/r/AskHistorians/wiki/profiles/celebreth
How did life change from 200 BC to 350 AD? https://www.reddit.com/r/AskHistorians/comments/1m3p8n/if_you_were_to_take_an_average_citizen_of_rome/
For more, you can listen to this episode: http://thehistoryofrome.typepad.com/the_history_of_rome/2010/03/88-a-day-in-the-life.html