Ask localisation in a form

So let's say I have a web app where people can add places they like. My database would look like this:

+-----------+----------------+--------------+---------------+
|    Name   |     Adress     |   Latitude   |   Longitude   |
+-----------+----------------+--------------+---------------+
| Blue Cafe | 8, Blue St, NY |  70,354635   |   47,56946    |
+-----------+----------------+--------------+---------------+

I can't ask my users to enter Latitude and Longitude.

I know Google Maps API can convert an adress to latitude/longitude, but:

• How can I ask an adress an know that it exists in Google's database?
• Can I show a map where people would click to locate the place?