Almost, hardly: gần như, hầu như (không)

Gần như means "almost, nearly" and goes before the verb or adjective: Em gần như quên hết rồi. I've almost completely forgotten. It describes a state that's nearly complete or nearly true: Quán gần như hết chỗ. The place is almost full.

Hầu như means the same and sounds a little more written, but two uses are common in speech. With không, it's "hardly, almost never": Tôi hầu như không ăn thịt. I hardly eat meat. With ngày nào cũng and the like, it's "almost every": Hầu như ngày nào em cũng uống cà phê. I have coffee almost every day.

Before xong (done) or a time, plain gần is enough: gần xong (nearly done), gần mười giờ (nearly ten o'clock).

Suýt is different: it's for something that nearly happened, once, and then didn't happen at all. Em suýt trễ means I was nearly late, but I wasn't. And for "most" before a noun, the word is hầu hết, not hầu như.