If you've downloaded the command-line client and have TypeScript installed on your machine, then go ahead and fetch the first problem.
exercism fetch typescript
In order to be able to submit your solution, you'll need to configure the client with your Exercism API key.
exercism configure --key=YOUR_EXERCISM_KEY
When you've written a solution, submit it to the site. You'll have to configure the command-line client with your exercism API key before you can submit.
exercism submit PATH_TO_FILE