How do I reliably make a lane push by itself?

What do I have to do, and when, to make a wave of minions start building up so it pushes a lane by itself?

I am not talking about split pushing, where I am constantly in the lane I want pushed.

I want to set up a lane so it starts pushing with a pile of regular minions so I can join my team to siege another lane 5 vs 5 or to do map objectives.

It takes time, and the self control not to kill all those minions ;) You'll find most answers in this Lol Forum topic

Long story short, you shall kill only the ennemy's mage minions first. They are the weakest, but they hit the hardest (twice as much as the melee minions if I remember correctly). Your minions will spend quite a bit of time to kill the solid melee minions, just enough time to let the next wave reach them, you'll then have 4-5 minions left in your first wave + the 6 (or 7) of the next wave. If the initial fight is in your part of the map, you may eventually kill the ranged minions of the opposite second wave, in order to build a hardcore minion wave, but it takes time.

Have fun.