EPrints 3.4 has the same prerequisites as 3.3.
We advise installing eprints into /opt, and running apache as the eprints user

As the root user download both eprints-3.4.0.tar.gz and eprints-3.4.0-flavours.tar.gz and put them into /root/
Then also as root install the files:

cd /root
tar xvzf eprints-3.4.0.tar.gz
tar xvzf eprints-3.4.0-flavours.tar.gz
cd eprints-3.4.0
./configure
make install

# change to the eprints user
su - eprints
cd /opt/eprints3

# to create a minimal repository
bin/epadmin create zero

# or to create a publications repository
bin/epadmin create pub

For upgrade existing repository from EPrints 3.3.12 and later versions, please refer to 
https://wiki.eprints.org/w/Upgrading_3.3.12%2B_to_3.4