What's the minimum slope I need to install asphalt shingles?

Don't go lower than 2:12 which means two inches of vertical rise for every twelve inches of horizontal run. Anything between 2:12 and 4:12, you should consider installing two layers of #15 felt underlayment, reducing the exposure of the shingle - the exposure being the part of the shingle that remains visible after installation, or both. In lieu of both of these, you may want to install a self-adhering ice and water underlayment over the entire deck surface.