How does the paper tape or silicone tape help a tummy tuck scar? Also how are you supposed to apply it?

Scars are mainly collagen with no oil glands.  Therefore, they will dry out, microscopically crack an allow bacteria to fall into the cracks.  The bacteria will cause inflammation which leads to thicker scars.  Covering fresh scars with tape, silicone sheeting, or scar care products will keep the scar tissue from cracking so the scars will end up thinner.  Taking good quality vitamins and minerals also helps.

Paper tape and silicone tape can reduce the tension on the scar. Reducing tension results in a narrower or finer scar. Stitches in the deep layers of the soft tissues do the majority of this work but the tape helps externally.  Both paper tape and silicone tape will also prevent dehydration however silicone is much more effective. Trans epidermal water loss or dehydration of the scar increases the inflammatory response, which causes more scarring (Dr. Tom Mustoe). 
Paper tape can be applied over the scar and left for days. Silicone tape is applied over the scar and is usually removed before showering and reapplied afterwards. Most silicone products come with instructions describing the most effective ways to use the particular product.

Scarring is a complicated issue and varies from person to person.  It is a topic that should be addressed with your surgeon prior to your surgery.

I have tried various techniques for scar management.  Several years ago I did a study of 100 patients where silicone strips were used on one side, and paper tape on the other.  We have found that the paper tape worked just as well, was cheaper, and much easier to keep on, so this is what we now use