I am installing this printer on Ubuntu 13.10 just a week after 13.10 was released.
The drivers that Ubuntu tries to install by default, from the gutenprint project, fail. So I have to do it manually. Possibly if Ubuntu polishes and fixes the default installation method it may work in the future, as it was working by default in Ubuntu 13.04.

I am connecting to the printer via USB. In a later version of this tutorial I will explain how to connect via LAN.

I download these two files from the mentioned Brother's pages.

dcp8110dnlpr-3.0.0-1.i386.deb 

dcp8110dncupswrapper-3.0.0-1.i386.deb

In theory I can choose to install either the CUPS one or the LPR one. But it seems that if you choose to install the CUPS one, you have to install first the LPR one and then the CUPS one. And this is what I am going to describe, how to install both in order to get the CUPS driver to work. I am choosing CUPS as it is a more modern system.

Procedure:

Install Apparmor utils (with sudo agt-get install apparmor-utils
or with the Ubuntu software centre)

sudo apt-get install apparmor-utils

Let's tell Apparmor (aa) not to complain (aa-complain) about CUPS
(cupsd package)

sudo aa-complain cupsd

Let's create a directory necessary for the installation. But in my
case Ubuntu replied that the directory was already present.

sudo mkdir /usr/share/cups/model

Let's install the LPR driver (of course you need to navigate with
the command line to the folder where you have donwloaded the driver
file) (Quick tip: Use "cd" to navigate in the command line, example
"cd Documents" to go to a subfolder called Documents inside your
present folder, or "cd .." to go to an upper folder)

sudo dpkg -i --force-all dcp8110dnlpr-3.0.0-1.i386.deb

Install cupswrapper driver

sudo dpkg -i --force-all dcp8110dncupswrapper-3.0.0-1.i386.deb

Check if the LPR driver and cupswrapper driver are installed

dpkg -l | grep Brother

This is the output I get in my computer for this command:

ii  dcp8110dcupswrapper                       3.0.0-1                                 i386         Brother DCP-8110D CUPS wrapper driver

ii  dcp8110dncupswrapper                      3.0.0-1                                 i386         Brother DCP-8110DN CUPS wrapper driver

ii  dcp8110dnlpr                              3.0.0-1                                 i386         Brother DCP-8110DN LPR driver

ii  printer-driver-ptouch                     1.3-6                                   i386         printer driver Brother P-touch label printers

I am connecting to the printer via USB. Now let's check via the CUPS
interface if the printer is present. Let's open a browser and go to:

localhost:631/printers

Following the official instructions we should

Check if the Device URI of your printer is "usb://Brother/(your
printer's model name)"

If the device URI is different from the example above, please go to
"Modify Printer" of your printer to select proper device and driver
How to do this: Click on the printer's name; you are sent to another
page, that should display the URI in the "Connexion" area.

The output I get from the CUPS interface in my computer is:

usb://Brother/DCP-8110DN?serial=E70745A3N358848

Also as a side note, in my case, the first time I printed a page, a first page was printed saying that I installed the wrong driver, but I know I did everything correctly. Also this page has not appeared again:

In my computer the printing works well.

------------------------------------------------------------------------------------

Scanning:

We need 2 files, the scanner driver (32bits or 64bits) and an extra file.

Driver file name on July 2014.

32 bits: brscan4-0.4.2-3.i386.deb

64 bits: brscan4-0.4.2-3.amd64.deb

Extra file name on July 2014:

brother-udev-rule-type1-1.0.0-1.all.deb

1) Getting the driver file

You need a 32bit or 64bit version of the driver.
You can check you Linux version by typing on a terminal uname -a

This is the output of uname -a in a 32bits system: (notice i686 and/or i386)

Linux tommy 2.6.38-8-generic-pae #42-Ubuntu SMP Mon Apr 11
05:17:09 UTC 2011 i686 i686 i386 GNU/Linux

This is the output of uname -a in a 64bits system: (notice x86_64)

Linux webserver 2.6.28-19-server #64-Ubuntu SMP Wed Aug 18 22:43:50
UTC 2010 x86_64 GNU/Linux

After you know if your system is 32bit or 64bit go to your printer's drivers page, accept their EULA, and download your driver.

In July 2014 the driver names are respectively:

32 bits: brscan4-0.4.2-3.i386.deb

64 bits: brscan4-0.4.2-3.amd64.deb

2) Getting the extra file:

After you have downloaded your driver you will see in that page there is a procedure about how to install the driver, and in the 5th item of the description there is a link that says "Use your usb-connectrd scanner by a normal user", click on it, then you will be taken to another page with information about several linux distributions, for Ubuntu 10.10 to 13.10 (valid also for more recent ones, such as the current one now, 14.04) there is a link that says "1. Click here to download the file.(brother-udev-rule-type1-1.0.0-1.all.deb, ver.1.0.0-1, 2KB)" click on it and get the 'extra' file

brother-udev-rule-type1-1.0.0-1.all.deb

Now we have our two files, our driver file (32 bits or 64 bits) and the 'extra' file. We can now install the drivers.

3) Prerequisite before installing the driver files: We need to be sure our computer has installed the two following files, a) sane-utils b) tcsh

Install them via Ubuntu Software Centre or with the following command in a terminal:

sudo apt-get install sane-utils tcsh

4) Install the driver with your printer turned on and connected via USB.

Open a terminal and go to the folder where you saved your driver files, and execute:

For the 32bits version:

sudo dpkg -i --force-all brscan4-0.4.2-3.i386.deb

For the 64bits version:

sudo dpkg -i --force-all brscan4-0.4.2-3.amd64.deb

5) Install the extra file so not only the superuser can use the scanner:

dpkg -i brother-udev-rule-type1-1.0.0-1.all.deb

6) Check if the scanner is installed by typing on a terminal:

dpkg -l | grep Brother

The output in my computer for this command is:

dpkg -l | grep Brother

ii brscan4 0.4.2-3 i386 Brother Scanner Driver

ii dcp8110dncupswrapper 3.0.0-1 i386 Brother DCP-8110DN CUPS wrapper driver

ii dcp8110dnlpr 3.0.0-1 i386 Brother DCP-8110DN LPR driver

ii printer-driver-ptouch 1.3-8 i386 printer driver Brother P-touch label printers

Restart the computer and check your scanning. I am using simple scan and it works properly.

Note: Remember to set up your printer via its physical interface, via its cursor rubber buttons and small screen

A) the resolution at which you want your docs to be scanned and

B) the format of the file that will send to your computer: jpg or pdf.