Go to File menu > Import Photos and Video. That will bring up the import dialog. If it fills the screen, look in the top right corner and you'll see the File Handling panel. If the Import dialog doesn't fill the screen, press the small arrow in the lower left corner to enlarge it.
If what areohbee doesn't completely solve the issue and wha you want is to display the file name of the pics while in the Library module for example, go to View Options (right click on the viewer in Library Mode is the easiest IMO) and choose the info you want displayed (file name, file base name, date etc...) from the drop menus for "Top" and "Bottom Labels" in "Compact Cell Extras" and make sure the "Top Label" and "Bottom Label" (either or both) are checked.
It works the same if you are displaying "Expanded Cells" but you'll be choosing from the 4 possible data fields in the "Expanded Cell Extras" area.
Check both the Grid view and Loupe view tabs to make sure you have the info you want displayed on both views later on (in Loupe view tab you'll want the "Show Infor Overlay" activated, and you can choose whether the info is displayed constantly or briefly when changing images). Your choice in the Loupe View tab will be mantained when you access the Develop mode too.
Hope that helps.
The easiest way, when importing, is to click the "don't import suspected duplicates? as LR uses several parameters (file size and name, metadata etc...) to see if the pic to be imported matches any other already present in the catalogue.
If you have the same picture with different names (for example you downloaded a card and renamed it, and then you're importing it again with the original file name), LR will import them. If you suspect this may be the case, you can always stack the images by shootin time for example, and compare them (and get rid of one of the pics)
If a picture is not in the catalogue (for example, if you imported it with LR in a batch of pics but then removed from the catalogue that specific image), LR will import it to the catalogue.
Sometimes LR may import duplicates by accident (for example if you forgot to check the "don't import suspected duplicates" box). When this happens, LR usually appends a "-2" to the file name, so doing a text search for "-2" (or other numbers) works good. If you did change the file names I stll think shooting time stacking works rather well (especially as you get a global view of your pics), but if your catalogue is big and you have to go through it it might be a bit of a bother.
If all else fails, there is a special plug-in to find duplicates. You can try it for free but a license key must be purchased. I haven't tried it myself, but here's the link should you care to do so.
How do I import all of my files from Picassa into Light Shop room without drama.
1. Click the big giant 'Import' button in Library Module.
2. Make sure nothing is checked on the right side, and everything is set to 'None' or is "blank"...
3. Select photo source(s) on left.
4. Click 'Add' at the top.
5. Click 'Import'.
0. Install Ottomanic Importer plugin.
1. Select 'Import Folders or Files' from 'Library Menu -> Plugin Extras'.
2. Browse to and select folders containing photos to import.
3. Click 'Choose Selected'.