On the sides of the Tetris grid is the Frenzy meter. Clearing lines will add to the meter, and dropping too many pieces without clearing a line reduces the meter. Once in Frenzy, any block that gets cleared converts the remaining portions into single blocks for easy cascades, and lines are continuously added underneath the stack. Frenzy is continued by clearing lines, where every block that doesn't clear a line detracts from the bar until Frenzy is done.
The goal is to fill the meter without dropping too many blocks between clears. Don't worry about building the stack up, as continuous Frenzy activation will keep adding more. Rather than going for Tetrises all the time and clearing four lines at once as if you were going for score, it's advisable to go for single lines to clear quickly. Hold straight blocks as long as you can.
As soon as it activates, stop clearing lines and start building up the stack; if you can create a Tetris opportunity to drop that straight block into, go ahead and do it. Once Frenzy deactivates, clear the lines you just built up and try to retrigger Frenzy quickly.
For free powerups, the most useful one will be Quake. This will help break up the stack and drop blocks into holes made. Magnet could also be useful to create Tetris opportunities. Build the stack so there's a long line for straight blocks, then use two in a row: as soon as you get one, drop it, then use the held one.
For paid powerups, Avalanche does wonders. Avalanche drops three rows of single blocks which tend to have a cascading effect when they clear lines. These cascades frequently lead to Frenzy mode. Lucky Sevens gives you the seven most optimal pieces you could get, which will aid in clearing lines quickly. Three Strikes could be used in conjunction with Magnet to make tall stacks and strike them down quickly.