Break down Lateral Torsional Buckling for me
Lateral Torsional Buckling (LTB for short) for Steel Beams has been explained in depth on this page. In short, LTB is a failure criteria which can limit the flexural capacity of a beam when the beam is spanning long distances with no lateral bracing.
This page is dedicated to showing how to solve for lateral torsional buckling of compact sections using the 13th edition AISC Steel Construction Manual. Even though most beams are compact, this solving for the LTB limits and subsequent Moment Capacities is a very tedious process (which translates in engineering terms to easy to make mistakes).
How to Understand LTB  
What assumptions have been made?
This is the first section of this page to emphasize that the following assumptions must be met for the following equation to work.
 For doubly symmetric Ishaped (includes double channel, Ibeams, etc.) members bent about their major axis.
 For compact sections
 Uses the 13th Edition AISC Steel Construction Manual (aka AISC 360)
How to solve for the LTB limits
Originally Taken From Steel Beam Lateral Torsional Buckling
Fig. 1: Moment Capacity during the 3 stages of Lateral Torsional Buckling (L.T.B.)
Three limits exist when solving for lateral torsional buckling (shown in Fig. 1 above):
 L_{b} < L_{p} which defines when a member is not subject to LTB
 L_{p} < L_{b} < L_{r} which defines when a member is subject to inelastic LTB
 L_{r} < L_{b} which defines when a member is subject to elastic LTB
where:
For Compact Cross Sections (most common):
Solving for L_{p}: L_p = {1.76{r_y}\sqrt{\frac{E}{F_y}}}

where:
r_{y} = The radius of gyration? about the weak axis of the cross section
E = The modulus of elasticity of the steel beam (e.g. 29000 ksi)
F_{y} = The yield strength of the steal beam (e.g. A36 has a yield strength of 36 ksi)
Solving for L_{r}: L_r = 1.95r_{ts}\frac{E}{0.7F_y}\sqrt{\frac{Jc}{S_xh_O}}\sqrt{1+\sqrt{1+6.76\left(\frac{0.7F_y}{E}\frac{S_xh_O}{Jc}\right)^2}}

where:
r_{ts}^{2} = \frac{\sqrt{I_yC_w}}{S_x} = \frac{I_yh_O}{2S_x}
I_{y} = The Moment of Inertia about the weak axis of the cross section (in^{4})
C_{w} = \frac{I_yh_O^2}{4} (for rectangular flanged doubly symmetric shapes)
S_{x} = Section Modulus? of the beam about the strong axis of the cross section (in^{3})
h_{O} = distance between flange centroids = d  t_{f} (in)
E = The modulus of elasticity of the steel beam (e.g. 29000 ksi)
F_{y} = The yield strength of the steal beam (e.g. A36 has a yield strength of 36 ksi)
J = torsional constant (in^{4})
c = 1 (for doubly symmetric Ishape) or \frac{h_O}{2}\sqrt{\frac{I_y}{C_w}} (for a channel)
C_{w} = warping constant (in^{6})
Note: For standard doubly symmetric Ishapes: r_{ts}, r_{y}, J, S_{x}, h_{O}, I_{y}, & C_{w} can all be found in Table 1 of the AISC 360 Steel Construction Manual^{[1]}. This makes these calculations much easier.
Solve for the flexural capacity of the beam
The flexural capacity of the beam will be broken into three sections:
 L_{b} < L_{p}
 L_{p} < L_{b} < L_{r}
 L_{r} < L_{b}
L_{b} < L_{p}
As you can see in Figure 1 above, when L_{b} < L_{p} the beam has no LTB instability and thus:
Solving for L_{b} < L_{p}: M_n = M_p = F_yZ_x

where:
F_{y} = The Yield Strength of the Steel (e.g. 36 ksi, 46 ksi, 50 ksi)
Z_{x} = The Plastic Section Modulus in the x or strong axis. Z_{x} is similar to the Section Modulus of a member (it is usually a minimum of 10% greater than the Section Modulus) (in^{3})
L_{p} < L_{b} < L_{r}
When L_{p} < L_{b} < L_{r} the beam has inelastic LTB and thus:
Solving for L_{p} < L_{b} < L_{r}: M_n = C_b\left[M_p  (M_p  0.7F_yS_x)\left(\frac{L_b  L_p}{L_r  L_p}\right)\right] \le M_p

where:
C_{b} = Beam bending Coeeficient
M_{p} = M_{n} = Maximum Flexural Capacity
F_{y} = The yield strength of the steal beam (e.g. A36 has a yield strength of 36 ksi)
S_{x} = Section Modulus? of the beam about the strong axis of the cross section (in^{3})
L_{b} = Unbraced Length (bracing must resist displacement of the compression flange or twisting of the cross section)
L_{p} = The limit between no LTB and Inelastic LTB for a compact section
L_{r} = The limit between Inelastic LTB and Elastic LTB (ft)
L_{r} < L_{b}
When L_{p} < L_{b} < L_{r} the beam has elastic LTB and thus:
Solving for L_{r} < L_{b}: M_n = F_{cr}S_x \le M_p
F_{cr} = \frac{C_b\pi^2E}{\left(\frac{L_b}{r_{ts}}\right)^2}\sqrt{1+0.078\frac{Jc}{S_xh_O}\left(\frac{L_b}{r_{ts}}\right)^2}

where:
F_{cr} = Elastic Buckling Stress (psi, ksi, etc.)
C_{b} = Beam bending Coeeficient
E = The modulus of elasticity of the steel beam (e.g. 29000 ksi)
L_{b} = Unbraced Length (bracing must resist displacement of the compression flange or twisting of the cross section)
r_{ts}^{2} = \frac{\sqrt{I_yC_w}}{S_x} = \frac{I_yh_O}{2S_x}
I_{y} = The Moment of Inertia about the weak axis of the cross section (in^{4})
C_{w} = \frac{I_yh_O^2}{4} (for rectangular flanged doubly symmetric shapes)
J = torsional constant (in^{4})
c = 1 (for doubly symmetric Ishape)
S_{x} = Section Modulus? of the beam about the strong axis of the cross section (in^{3})
M_{p} = M_{n} = Maximum Flexural Capacity
Important: Don't forget that M_{n} is the nominal moment which still needs to be divided by Ω_{b} (for ASD = 1.67) or multiplied by ϕ_{b} (for LRFD = 0.9) to find the design flexural strength.
A Spreadsheet to make everything easier
Finally!!! All of these meaningless variables in complex equations broken down into a spreadsheet that is easily used. You can find the spreadsheet and explanations on how to use it on the Steel IBeam LTB Spreadsheet page. Hopefully this spreadsheet will make quick work of a very complicated process (Any process that requires six equations and more than 20 variables is considered quite complex in my own humble opinion.
References
 American Institute of Steel Construction, "Steel Construction Manual 13th edition", 2005
 This Section is thoroughly covered in Part 3 of the AISC Steel Manual and in Chapter F2 of the Specifications (AISC 360)
 Table B4.1 in the Specifications (AISC 360) has also been referenced to find λ_{p} & λ_{r}.
 Most of the required variables to solve the above complex equations (for standard sized beams) can be found in Table 1 of the manual.