hard work and determination

"Hard work" means doing work that is difficult. "Determination" is a personality trait that some people have. Determination allows a person to continue to work hard on something, even though they might want to quit. An example of determination is an athlete who wakes up at 5:00 in the morning every day to train for two hours before going to school.

"Hard work and determination" often appear together.

(something) paid off

When you spend time or money on something risky, you hope that there will be a good result. If so, you say that it "paid off". For example, the father of a professional musician might say:

I'm glad to see that all those years of piano lessons I put him through finally paid off.

You can talk about investments and projects at work with this phrase:

We're spending over fifty thousand dollars on these improvements. That may seem like a lot of money at first, but I'm confident that it will pay off down the road.

One other example of a situation you can use "pay off" in is when talking about trusting someone who might not be very trustworthy:

My trust in her paid off in the end, though. She ended up doing the right thing.

really

"Really" means "very" but is better for casual conversation. "Very" is correct in written English, but can sound a little formal and old-fashioned in spoken conversation.

I thought it was a really original take on the story.

Also, "very" can only be used to modify an adjective: 

It's very small.

I'm very tired.

"Really" can be used for adjectives as well as verbs:

It's really small.

I'm really tired.

I really wanted to go

Do you really think so?