A Lewis dot structure is a way to show how many outer, or valence, electrons an atom has, and also how the valence electrons of two (or more) atoms can interact to create a chemical bond.
To draw a dot structure for an atom, you must figure out how many valance electrons the atom has. To do this, look at a periodic table of the elements. Find the element, and then count how many spaces it is from the left hand margin of the table, skipping the d-block (transition metals). The number of boxes you counted is equal to the number of valence electrons. (There are instructions for this here.)
Once you know the number of electrons, write the element's abbreviation, and put that number of dots around it. You should start by putting one dot directly above the letters at 12 o'clock, then put a dot at 3, at 6, at 9, at 12 (which makes a pair), and so on until you run out of dots. There should never be more than 8 dots (4 pairs). Here's what bromine would look like according to these rules.