The oak sawdust is best used during primary fermentation and then left behind when racked into secondary. Using it after primary is more difficult, but still can be done. I would hydrate it with a little of the wine from the secondary before adding it, then stir it in. After you have added it, taste the wine every few days until it reaches an oakiness that you like, then rack again. The problem after primary is that it is harder to remove.
Sawdust works quickly because of the enormous amount of surface area it has exposed to the wine. Shouldn't take more than 1-2 weeks at maximum.
Another, cleaner alternative is to add oak beads to the secondary. Still quite a bit of surface area, but easier to control.
Good luck.