How do I give only the owner of a folder write/delete access?

Create a folder and run chmod (change file mode) to change the permissions.

mkdir folder
chmod 755 folder

actually this is the default.

Changing permissions of the content of an already existing folder:

# Give write access to owner
chmod -R u+w folder
# Revoke write access of group and others
chmod -R go-w folder
# Give read access to everyone
chmod -R a+r folder

Or together in one command (thx @chrylis)

chmod -R u=rwx,g=rx,o=rx folder

Give the owner user all permissions and everybody else only read and execute, and take away write permissions for everything inside:

sudo setfacl -Rm u::rwX,g::rX,o::rX /path/to/directory
sudo setfacl -Rdm u::rwX,g::rX,o::rX /path/to/directory

The first sets the permissions for existing things, and the second sets the default permissions for anything created in the directory. rwX grants all permissions (X grants execute if a directory or if already executable).