Half the battle is determining earth pressures. You just have to get several publications and extract bits and pieces from the following:
"Smith's Elements of Soil Mechanics" 2007
"Soils & Foundations" by Liu & Evett(any edition after 1995) & My favorite "Foundation Design" by W.C. Teng, 1962.
Whatever you do, do not buy software at this early stage. Do it by hand and get a feel for the variables. Using a computer will give you elegant output, but you won't be able to "feel" if depth of embedment for example is off by 5 feet or not.
The mentioned books will give you the geotechnical inputs. What they should add, is to always factor your passive resistance. I use FS 1.25 for temporary walls, & FS of 1.5 for permanent walls. Further, limit your passive resistance to say 5 times the Equivalent fluid pressure. I leave the active Equivalent fluid pressure as is.
As RonRoberts, you can equate the active and passive pressures and get a polynomial to solve. I found it easier to get my embedment depth using: d= H / (kp/Ka)^0.333 - 1
note, H is shoring ht which is the only variable in the numerator, and all the other stuff is in the denominator. Kp & Ka are passive and active Rankine earth pressure coefficients.
Smith's book will give you equations on getting maximum moment. I use 0.6 times the steel yield strength to get the required section modulus. Then choose a beam with slightly larger section modulus.
Then comes lagging design, Ratay's "Handbook of Temporary Structures" has a good coverage on lagging design. Then something most designers forget, the deflection of the soldier beam at the ground surface. Lastly, you need to confirm if your numbers are reasonable, for that you can compare with Caltrans Trenching & Shoring examples, CivilTech's software manual or post it back here and we will comment on it.