Welcome to our wonderful hobby/obsession! With pellets you will get several different opinions. Some on here prefer to loosely bag their kettle hops, some prefer to just let them go free range in the boil (this is what I do). I assume you are referring to using a strainer as you pour from your kettle to your fermentation vessel to separate the leftover hops from your wort.
I have a drain valve on my kettle and I do a manual whirlpool before chilling with my big stirring spoon, which tends to settle most of the hops and other sediment in the center and reduces the amount that makes it into my carboy after running through my CFC. For big Double IPA's and highly hopped pale ales, I use a whirlpool with an immersion chiller run through my pump for a hopstand before chilling. I also toss the hops in free range for this and have never had my pump clog as most of the sediment stays in the center while draining after a whirlpool.
As for dry hopping, I keg so I use a muslin bag for my hops and toss the bag in the keg to prevent clogging. If you are bottling, you can also do this, although some others on here toss them in free range before bottling. Some recipes call for multiple rounds of dry hops, so you can play around with methods to determine which you like best.