Main Reference Zee (Quantum Mechanics in a Nutshell).
1) Global symmetry
A global symmetry means that the Lagrangian is invariant by a transformation whose parameters are constant.
For a continuous global symmetry, if the symmetry of the Lagrangian is the group $G$, and if the symmetry of the vacuum is the group $H$, a subgroup of $G$, you have ($dim G-dim H$) Goldstone bosons.
For instance, take a complex scalar field $\Phi$ with a Mexican hat potential , so that the total Lagrangian density is $L = \partial \phi^\dagger \partial \phi + \mu^2 \phi^\dagger \phi - \lambda (\phi^\dagger \phi)^2$.
The group symmetry is here $G=O(2)$
Define $\phi = \rho e^{i\theta}$
Breaking the symmetry means choosing for the vacuum the minima for the potential, and a particular angle, that is :
$\rho_V = v, \theta_V = \theta_0$
The group $H$ is trivial here.
Define :
$\rho = v + \chi$, where $v = \sqrt{\frac{\mu^2}{2\lambda}}$
Developping the Lagrangian, you get a term $v^2(\partial \theta)^2$, which is the dynamical part for a massless field $\theta$, so $\theta$ is our Goldstone boson (There is one because $dim G - dim H = 1 - 0 = 1 $).
So, we see, that spontaneous symmetry breaking could arise in a global continuous symmetry.
2) Local symmetry
A local symmetry means that the Lagrangian is invariant by a transformation whose parameters are functions of space-time.
"Gauging" means (continous) local symmetry.
So you don't need "gauging" to have a spontaneous symmetry breaking.
With a local symmetry, some of the Goldstone Bosons are "eaten" by the Gauge field ($A_\mu$), so that these gauge fields (which are massless) become massive. In a 4d space-time dimension, a massless Gauge field has $2$ degrees of freedom, while a massive gauge field has $3$ degrees of freedom. To do that, the Gauge field has to "eat" one degree of freedom (one Goldstone boson)
3) Global symmetry as a special case of Local Symmetry
In the set of local symmetry, global symmetry is a very special case (a very special subset), where transformation parameters are constant. So, if you want, you can consider that global symmetry are "included" into local symmetry.