Briefly:
(1) Put the inequalities and objective function in standard form by adding slack variables and writing the objective function in the form P-..........=0
(2) Form the intial tableau.
(3) Select the most negative entry in the objective row.
(4) Consider the column that corresponds to the most negative entry. Calculate theta values [(value)/(column)] for each row other than the objective row and choose the smallest.
(5) The pivot lies at the intersection of the row with the smallest theta value and the column with the most negative entry in the objective row. Circling the pivot. This variable (eg x,y,z) at the top of the pivot column is called the entering variable while the slack variable (eg r,s,t) at the far left of the row of the pivot is called the leaving variable. In the new tableau the entering variable replaces the leaving variable.
(6) Divide all entries in the pivot row by the pivot.
(7) Consider a row other than the pivot. You need to add a suitable multiple of the value of the pivot box(which is now 1, as you divided the pivot row by the pivot) to the value in the pivot column of the row being considered so as to make the entry 0.
(8) Working your way along the row being considered, add the SAME multiple as before of the value from the pivot row, but you're adding multiples from the column of the pivot row corresponding to the column in the row being considered. Repeat until the row being considered is now finished.
(9) Repeat (7)+(8) for all rows other than the pivot row.
(10) The tableau has been revised. If there are no negative entries in the objective row the process is complete and you can interpret the results. If there are negative entries then i'm sorry but you have to repeat (1)-(10).
Hmm. Looking back that doesn't seem that brief. Feel free to ask about what you're unsure of.