Other replies have covered everything about increasing pop growth on planets conventionally. However, if you want insane numbers of pops without having to pay any attention to pop growth there are two options:
1.nihilistic acquisition, for which you need either authoritarian or xenophobic ethics. As long as you have a casus belli, declare war with bombardment setting on your fleets to raid, empty the enemy's planets of pops and then white peace, pick your next target, rinse and repeat and you can keep farming pops from AI empires as long as want, long after ordinary planetary growth rate has effectively slowed to zero on your own planets.
2.the slave market. Currently, because AI empires buy up slaves almost immediately after they come on the market, the only way to buy slaves is to put the game on its slowest speed, keep the slave market screen open and your finger hovered over the pause button and as soon as a pop comes up for sale you pause and then buy it. This is painful micromanagement but if you can bear it then you will probably get somewhere in the region of 15-20 odd new pops a year depending on galaxy composition, although the rate slows down late game. I did see in the patch notes for 3.3 that they are going to adjust how AI empires buy slaves so they may stay on the market for longer in the new patch.
Just to add, if synthetic ascension is your thing and you want to assimilate your newly acquired pops then spread them around your planets rather than keeping them all on one planet, as you will then assimilate the pops at a much faster rate.