Add 1 extra table at a time until you are comfortable and then add another etc etc
Pretty much this.
You have to learn to walk before you can run. The brain needs time to adapt and be trained to process the information quickly enough to play more and more tables.
Various software can make life a lot easier for this, table ninja and hem really help me out.
Just don't push yourself too quickly imo, it will come but a lot of people do it too quickly and don't even realise they are playing really sub optimally and hindering their evolution as a poker player by doing so.