First, since you get the data from a prompt separated by comma, you need to split the string to make it an array. To do so :
var infos = prompt("Enter user's name,surname,telephone number,Email keeping the order and separating words by a comma"," ")
var infosArray = infos.split(',');
dataBaze.push(infosArray);
The split method lets you take a string and divide it into chunks with the delimiter you pass into the function. So ".split(',')" finds every instance of a comma and takes what is before it and push it into an array. When the full string has been parsed, it returns the full array.
From there, each cell of the array will contain every information in its own sub-cell (dataBaze[0] may contain something like
['MyName', 'MySurname', '555-555-5555', 'myemail@email]
So let's say you want the name you could use "dataBaze[0][0]", and so forth.
However, there are a couple of ways to make things a little bit easier to read and to maintain, such as inserting an object into the array, something like so:
var user = {name:'', surname:'', telephone:'', email:''};
user.name = infosArray[0];
user.surname = infosArray[1];
user.telephone = infosArray[2];
user.email = infosArray[3];
dataBaze.push(user);
Then you can access infos like so :
document.write("My name is " + dataBaze[0].name + ", and my surname is " + dataBaze[0].surname + ". You can call me at " + dataBaze[0].telephone + " or contact me by email at " + dataBaze[0].email +". Thanks!");
What we've done here is create an object ({}) which is basically a keyed array (it is more but let's not get too deep for no reason).
So when you come back to your code later, you don't have to guess every time which cell is what.
Edit: Just thought I'd add some explanation to the what and whys.
$("button").click(inputData());needs to be$("button").click(inputData);.