Suppose you have a function f, of a variable X.
You select a value for X, say x. Calculate the value of f(x) that is, the value of the function when X takes that value x. Then, instead of writing the result in a table, mark the point [x, f(x)] on the coordinate plane. Repeat with other values for X and join up the points.
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rule, table of values and graph
The graph of a continuous function will not have any 'breaks' or 'gaps' in it. You can draw it without lifting your pencil or pen. The graph of a discrete function will just be a set of lines.
y=x+1
Data is neither a table nor a graph, however, data may be presented in a table or depicted by a graph.
If you are looking at a graph and you want to know if a function is continuous, ask yourself this simple question: Can I trace the graph without lifting my pencil? If the answer is yes, then the function is continuous. That is, there should be no "jumps", "holes", or "asymptotes".