fast adjustment can be used

p "MyTwoColumnDataFile.dat" u 1:2 w lp ls 7 ps 2 lc 2

that is meaning use the first and second columns, with line and points ("w lp"), line style 7 (this style is the line with dots at the places where data are provided, "ls 5" would be rectangles, etc.), point size is 2 (here you can adjust the size of those dots), line color is 2 (set as you wish).