How to build CuraEngine?
I'm assuming you actually want to build Cura, rather than simply install Cura. If you instead want to install Cura, you can try sudo apt-get install cura-engine

The following instructions were tested on my own Debian 8 (Jessie) distribution; they should be mostly, if not entirely, the same, for Ubuntu. Note that I did not follow the exact steps as described on the github/Ultimaker/CuraEngine README.

Before we begin, let's make a build directory and do everything in there.

mkdir ~/Downloads/curabuild
cd ~/Downloads/curabuild


The instructions will be broken into 

1. Install dependencies

Some or all of these may already be installed on your computer. To be sure, we install them anyways:

sudo apt-get install git curl libtool dh-autoreconf cmake python3-setuptools python3-dev python3-sip sip-dev


2. Install protobuf


Clone and enter the protobuf git repository:

git clone https://github.com/google/protobuf
cd protobuf

Build and install for C++:

./autogen.sh
./configure
make # this will take some time
sudo make install

Install for Python 3:

cd python
sudo python3 setup.py install



3. Install libArcus


Clone and enter the libArcus repository:

cd ../..
git clone https://github.com/Ultimaker/libArcus
cd libArcus

Build and install

cmake .
make
sudo make install



4. Install CuraEngine


Clone and enter repository:

cd ..
git clone https://github.com/Ultimaker/CuraEngine
cd CuraEngine

Build and install

cmake .
make # grab a cup of coffee
sudo make install



5. Celebrate!

If all went well, you're done! You can now use the Cura engine via CuraEngine. Enjoy.