sign up for (something)

When you "sign up for" an event or activity, it means that you fill out a form that shows that you want to join. For example:

I signed up for an aerobics class at the gym.

We decided to sign up this year for the Walk Against Cancer.

You can also "sign up" someone else (usually a child) for an activity:

Maybe we should sign Gavin up for violin classes. 

there's (something)(doing something)

Use "there's ___" when you're describing a situation that's happening now:

There's someone at the door.

There's some food in the kitchen, if you're hungry.

Or something that's planned for the near future:

There's a game coming on at four.

It's also common to describe what something is doing using "there's":

There's a woman staring at you over there.

There's a humming noise coming from the refrigerator.

There's some cake sitting on the counter.

a tournament is held (at a certain place and time)

A "tournament" is a competition between lots of people or teams. Usually one person or team is named as the champion at the end of the tournament.

To talk about a tournament happening, use the phrase "be held", followed by the time of the tournament, the location, or both:

It's held between late March to early April each year.

Where is next year's tournament being held?

 Aside from tournaments, other events that are "held" include:

• conferences
• concerts
• meetings
• a hearing

I was thinking about (doing something)

Talk about a plan that you've considered with this phrase:

I've been thinking about signing up for an English writing course.

I've been thinking about dyeing my hair again.