I've recently become a sponsor and I don't really know how to send invites and stuff like that,Help?

That is something that you should talk to your CL about, mate :)

Ask them what they are looking for in recruiting and do your best from there. Also, ask them what exactly it takes to recruit, that's the reason they put the responsibility of a sponsorship within your hands.

As with what Mako said, it is usually something your Crew Leader should talk to you and inform you about regarding your new responsibilities.

On the Manage tab - Under the category of "Do Stuff" you will see "Sponsor". That shows your current associates, where they are etc. You can also invite new associates from this tab.

You should probably speak to your crew leader however about sponsorship.

Yes indeed as others have said you should have come to me or the leadership team who provided you with that ability.  We also have threads giving guidance on it.

Thanks to Morty for giving a quick overview.