Hi, and thank you for asking your question.
First off, please download iCloud on the new computer using the following link:
On the page that opens up, click on the blue Download button, and then download and install iCloud following the on-screen prompts.
After iCloud opens up, you will be prompted to sign in to your Apple account; once you sign in, your calendar, contacts and other data will be automatically synced onto iCloud on this computer itself.
If you need any further assistance with this issue, please be sure to reply back using the box below.
And, if you could kindly click on (and submit) one of the star buttons at the top of this page to rate my service, I would greatly appreciate it. Thank you.