Assuming, you have a Nexus, the internal memory should show up as a normal SD card would in other phones. When you connect your phone to a PC and then MOUNT it, it ought to show up as a removable drive.
You can use Aldiko - it's an eBook reader (currently freeware) that works well with epubs.
Copy the .epub file and drop it in your phone (after mounting)
Place the .epub file in * phone_directory/ebooks/import
Unmount, and start Aldiko
Press the menu key, and hit import, give it some time to copy the file, and you're done!
The newly imported book should now show up on your bookshelf.
The official FAQ might also help.
EDIT: An alternative (easier) method using the same app, available on Google Play.
I found that I could import the .epub without connecting the device to a PC. This was verified with a Nexus 7, which does not have an SD card.
- Navigate to Aldiko's main page. After selecting Files, you can browse the files on your device.
- Select the .epub file you want to read and select Import.
- The .epub will show up in the Aldiko library.