So You Want to Invite Someone You Do Not Know To Join You on LinkedIn
The first thing you must do is verify that they are on LinkedIn. This may sound easy, but there are a lot of people with the same name, so you must investigate further than a simple name search.
Now that you have confirmed that this is in fact a LinkedIn member and you have the correct person; how do you proceed?
The first option is to click on the individuals profile and see if you have any connections in common. If you do, then you might consider asking that person for an introduction. I say consider, because you never know how well someone actually knows a connection or if the relationship is a good one.
You can find my article on this part of your question Networking Referrals and Recommendations: by reviewing my list of articles on Ezine. The article goes into more detail on questions to ask of the person about their relationship and familiarity with your target and how to vet the contact.
The second option is to review the individual's profile for where they currently work or have worked in the past. Do a company search and see if there is anyone in your network that comes up as a current or former employee of these companies and ask them if they know the person and would facilitate an introduction.
Third, from the individuals profile find out if they are members of any groups and consider joining the group. Once you are in the group you could send an invite saying that you belong to the same group and that you have heard great things about the individual and that you would like to connect.
Fourth, if you have their email address you can simply send an invite, but this one is a little tougher and I don't recommend it as a great option. If you do this you run the risk of receiving an IDK (I Don't Know) and it can cause invite issues with LinkedIn. They don't black list you, but anytime you try to go with a simple friend request you must provide an email address.
On that note if someone invites you to connect and you do not want to connect; be polite and archive the message; do not send an IDK!