Here is a systematic way to go about writing all of the stereoisomers for a molecule with several chiral centers. Start by drawing a zig-zag backbone, with one corner for each chiral center:
The orientation of the backbone doesn't really matter; however, a research project I was involved in once upon a time suggested that the vertical orientation is clearer for most people.
Now fill in a wedge bond and a dash bond on each corner, to generate the tetrahedral arrangement of bonds for each chiral center. Notice that the wedge and the dash at each chiral center are always both on the same side of the backbone!
We will use as an example the molecule CH3CH(OH)CHClCHBrCH3. Locate the stereocenters in this structure, and identify the ligands on each one. Next, attach the ligands to the chiral centers you just set up. If one of the ligands is a hydrogen (H) place it on the dashed bond. Following this procedure is guaranteed to produce a valid stereoisomer.
Now, imagine a mirror placed next to the structure you have created (the red line in the sketch below), and draw the reflection you see in the mirror:
Assign the configurations, which should all be opposite to the ones on the original structure, and you have generated the first pair of enantiomers. We're now going to use the first structure we created as a reference point to generate the rest.
Follow the same steps: draw the backbone, fill in the wedges and dashes, and attach the ligands. This time, however, switch the positions of the H and OH on the top chiral center. This will automatically generate the enantiomeric configuration at that site. Reflect in the mirror:
Assign the configurations, and you have the second pair of enantiomers, each of which is a diastereomer of the first pair.
Repeat the construction twice more, each time starting with your original SRR structure. First, change the middle chiral center:
and finally, change the last chiral center:
Here's the progression we have followed, summarized with just the configurations. We created SRR, essentially at random. Reflection gave RSS, its enantiomer.
Then we switched the first chiral center, to get RRR and its enantiomer, SSS. Next, we switched the second center, creating SSR and RRS. Finally, we changed the third center, making SRS and its enantiomer, RSR.
Like many of the problems we work, this one yields to a systematic, step-by-step approach, taking advantage of two inescapable rules of nature: