Two colleagues recently asked me about this so I figure more of you want to know as well:
When you see that someone has asked to connect to you 
in the top right corner of your LinkedIn page and/or you are not sure if the connection is worthwhile or you cannot place the name, here’s a little game plan to get more info from him or her to make a decision:
- click the person’s name. Next you see this:
2. click the cartoon speech bubble with the quotation marks in it (see above) and a text box opens:
3. click the curved arrow at the top right corner in the illustration above to reply to the person.
4. type in a message; press the keyboard enter key to send via LinkedIn:
►I happen to like the message I am showing in the illustration as it keeps the door open (but usually they just never bother to reply, telling me it’s not a real sincere connection request.)
Moral of the story: save me the work (and you too!) having to repeat connection requests to identify yourself after the fact. Just tell me upfront how we can help each other and give me the context of where we met.
Please act professionally in all impressions.
I set up my LinkedIn to provide email notification; I prefer to manage things that way even though it adds more emails to my in box.
I first check my contacts; then I search the email in case there were some interchange but the person did not get added to my contacts; sometimes I even double-check against Facebook (but I am better at adding Friends to my contacts). Finally I respond by email with a query based on how much information -picture, work experience, shared connections- the inviter shares. In part, I prefer to respond by email since I can include a promo on my ebook, The Public Ought To Know.