All the customizations proposed below will take no more than 5 minutes to implement once you know what to do. SharePoint is flexible, though not very user friendly, and sometimes it's just hard to find the correct button or menu item...
Also one more thing: as I understood from your comments, you don't know SharePoint well, so I tried to make the answer as illustrative as possible, and admittedly it is a bit overgrown with images. Nevertheless, ...
Here I assume you have some existing SharePoint list with data filled in, something like this:
So if you go to list settings (Ribbon -> List Tools -> List -> List Settings) you will see two columns, Name and Last Name:
Add additional columns into this list. As in your question, let's add Address and Phone as a simple text fields (this will make them appear as text boxes). Make sure the "Add to default view" checkbox is not checked:
In this case the view will be the same as on the first picture, but if you open view or edit dialog on the list item, you will see there are also Address and Phone fields there:
Usually you go to edit form by clicking "Edit" in context menu or by selecting item first, and then clicking "Edit item" on the ribbon:
At this point you might want to consider if it is ok for you and stop here.
But if you still want to have a separate column with edit link, you will need to open SharePoint Designer and slightly customize the list.
Navigate to this list under List and Libraries:
Then under "Views" group click All Items.
You will see your list view. On ribbon, find "Add/Remove Columns" button. Click it and then add "Edit (edit link)" column to the view:
The result will be something like this:
It is very easy to change the title of the column and replace edit icon with some text. For title, click to the title text and then in Properties enter new title enclosed in apostrophes:
Then, click on edit icon, and below in the status bar select img tag and click Insert HTML:
Type "Details" instead of default "<>" text. Click accept icon, and then again select edit icon and hit delete. You will get something like this:
And in browser it will look like this:
Also if you don't want form to appear in a modal dialog, and prefer to redirect user to a separate page, this can be configured in List Settings, under Advanced Settings -> Dialogs -> Launch forms in dialogs (select "No").
It is also very simple to customize edit form if you want i.e. make "Name" and "Last name" not editable, and anything else. You have to learn SharePoint and practice with SharePoint Designer for few days, and maybe learn a bit of XSLT, but in the end you will be able to create almost any imaginable view and any kind of form for a SharePoint list.