I don't strain my wort usually- but if I wanted to because of a ton of debris, I'd use a sanitized "paint strainer" bag that you can get at home depot and Ace. You line your fermenter bucket with the paint strainer, pour the wort in, and then lift out the paint strainer. Do it near the sink so you don't drip all over the place. For a carboy, I guess a hand held strainer and funnel is the only option.
I use a hops spider for pellet hops in my boil kettle if I have a ton of them. If I don't have a ton, I just let them settle out in the fermenter.