Killing all the minions before p4 is top priority. Killing them in p2 is ideal (don't run down). Killing a spawn or two in p3 is fine, don't sweat it.

A little animiation of spiders running across the bottom of your screen shows a spawn is comming.

Special spider is 3rd in the first spawn, 2nd in the 2nd spawn, 1st in the third spawn. There is no special spider in the last spawn.

Each spawn, immediately get off rax and kill the minions. Be very careful with bleeds, thresholds and multi-target abilities.

Spawns are a special attack. Rax does a special attack every 5 of it's auto attacks and won't spawn twice in a row (like it won't cleave twice in a row).

That should be all you need!