Quick non rogorous way to obtain Feynman rules from a Lagrangian in a non abelian theory I have been told that a quick way to get the Feynman rules from a Lagrangian is to take an interaction term, forget about the fields and multiply an $i$. This works perfectly for example for QED but I wonder if there is an analogous non rigorous quick way to obtain the feynman rules of for example non abelian gauge theories.
 A: 
This works perfectly for example for QED

No, it doesn't. You can get the interaction vertex, but the photon propagator is still ill-defined. In order to get everything up-and-working you have to introduce an additional gauge-fixing term in the Lagrangian:
$$L_{\text{gauge-fixing}} = \frac{1}{2 \alpha} \left( \partial_{\mu} A^{\mu} \right)^2 $$
Only with this additional (unphysical and non-gauge-invariant) term can you obtain Feynman rules by 'looking' at the Lagrangian. There is a beautiful mathematical approach (Faddeev-Popov method), which is usually used to show that this gauge-fixing term can be added.
No to the N/A gauge theories. First, because the curvature is now modified by an additional Lie algebra commutator
$$F_{\mu \nu} = \partial_{[\mu}A_{\nu]}+[A_{\mu};\,A_{\nu}],$$
we get two extra terms in the Lagrangian
$$ L = -\frac{1}{2g} F_{\mu \nu}F^{\mu \nu} = L_0 + ... (\text{~} A^3) + ... (\text{~} A^4) $$
which give us two interaction vertices (3-valent and 4-valent).
The propagator is ill-defined, though. Performing the Faddeev-Popov procedure, we get the gauge-fixing term (just like in the Abelian case), but we also get new dynamical fields -- Faddeev-Popov ghosts. These are unphysical and can be thought of as aspects of specific gauge fixing.
They interact with gauge bosons via the 1-boson + 2-ghost interaction vertex. More details (including expressions for propagators and vertices) can be found in almost any QFT textbook (e.g. Peskin-Schreder).
