It is very important to make sure all utensils/bowls and whisks are grease free.  Squeeze a lemon or use some vinegar to wipe down everything that would touch the buttercream!

I like taking out my eggs and submerging them in a bowl of warm water, I have had much more success making Swiss Meringue Buttercream (SMB) using warm eggs and room temperature butter. 

Seperate the egg whites from yolks.  (Make certain no yolk gets into the whites as this could cause the meringue to flop.)  Place egg whites in a heat-proof mixing bowl set over (not in) a pan of simmering water.  Slowly add the sugar whisking as you add.  Whisk the mixture until it is warm and no granules of sugar can be felt between your fingers.  Just lift the whisk and "pinch" the mixture until it feels completely smooth.  This will take approximately 3-4 minutes.  Remove from heat and place on your electric mixer.

Mix the egg whites-sugar mixture on medium high until the bottom of the bowl feels cool to the touch and until the mixture reaches "stiff peak".  This will take approximately 8 minutes.  Make sure meringue can hold its shape on the whisk before continuing to the next step and adding any butter!

Reduce speed to medium-low and add pads of butter 2-3 tbsp at a time mixing well between until all butter is added.  Add vanilla and beat on medium-high for 4-5 minutes until smooth and silky.  If buttercream appears to separate at any time just mix on medium high until smooth again.  Buttercream can be refrigerated up to 3 days or frozen up to 2 months in an airtight container.  Bring back to room temperature and beat slowly before using again!