Building a staircase out of bricks is easy enough, but uses a lot of brick pieces, as zovits already answered. If you want to achieve something faster, with fewer pieces, you could look into the spiral-staircase-piece
or the regular staircase piece.
The spiral staircase piece combines with some plate+pin pieces (bottom, top) and some posts. You can connect as many posts together as you want using a pin.
The advantage of using the spiral staircase is mainly the simplicity of it; it's not that versatile a piece, but it works for its purpose and does have a nice round edge. Plus the stairs can be rotated, which allows for a "hidden staircase" feature.
The advantage of using the regular staircase piece is that it is very sturdy and it takes up very little space. You can build a similar staircase using the inverted slope and some 1x4 plates but it isn't as strong (and it's slightly taller).