Use git clone with the --depth option set to 1 to create a shallow clone with a history truncated to the latest commit.
For example:
git clone --depth 1 https://github.com/user/repo.git
To also initialize and update any nested submodules, also pass --recurse-submodules and to clone them shallowly, also pass --shallow-submodules.
For example:
git clone --depth 1 --recurse-submodules --shallow-submodules https://github.com/user/repo.git