SUMMARY
You can export selected prospect data directly from your campaigns either via CSV file sent to your email or push data via webhook.
In order to export data from campaign:
Go to Campaigns from the main navigation menu and select the campaign
In People tab, open Filter selection and enter the filters you want
You can select all filtered people per page OR select very specific people. Open Action tools.
Click on CSV Actions and choose between the 5 export options
If you chose to send CSV via email, ensure to provide the correct email address, select if you wish to include the last message with prospects and click Send
If you chose to push data via webhook, select the webhook from the drop-down list and click Send.
More about webhooks, learn here.
Note: In one go, you can export around 1MB size file which is around 2500 prospects
You can also export a CSV from the Search menu and My Network. Click on each to learn how.
IN DETAIL
In order to export a CSV from a campaign, go to Campaigns from the main navigation menu and select the campaign:

In People tab, open Filter selection and enter the filters you want (such as campaign status, tags, conversation status or keywords).

You can select all filtered people per page by ticking the box next to "Picture" OR select very specific people by ticking the box next to their profile picture one by one. Open Action tools:

Click on CSV Actions and choose between the 5 export options:

Mail selected contacts as CSV
Mail all filtered contacts as CSV
Mail all contacts as CSV
Export selected through webhook
Export filtered contacts to webhook
After you choose the option you want, you will be sent a CSV to your email address used to sign in to Prospect Labs by default.
If you wish to select a different email to receive the CSV file to, please ensure to make a correct address entry, click Send:

Here, you can also select if you wish to include the last conversation message with those leads by clicking "Include message" box
Likewise, if you selected to push the data via webhook, you would have to select the webhook from the drop-down list and click Send:

More about webhooks, learn here.
Note: In one go, you can export around 1MB size file which is around 2500 prospects
You can also export a CSV from the Search menu and My Network. Click on each to learn how.