How far in advance can active duty service members from all branches start training or looking for employment?

Enlisted Members may be released through a 4187 under the attached MILPER Message up to 6 months early from ETS. This is contingent on a letter from an employer with a bona fide job offer: http://www.ssi.army.mil/!CareerAdvisor/Messages/Milper%20Message%2015-019%20Enlisted%20Voluntary%20Early%20Seperations%20Program.pdf

Officers MAY be able to start work on transition leave. They will need an ethics brief and a visit to JAG if it is a government contractor.

Transition assistance is telling people 6 months out for applying to jobs in earnest. Up to 12 for federal jobs.

I am going through SFL TAP right now. There are tons of info and websites. Tools and calculators. VA stuff, DoL stuff, commercial stuff. What can be done to help? Realistically help draft resumes and convert military experiences to civilianese. Explain to civilian employers what military qualifications, experience, and leadership really means.....And offer someone a no-shit job for a realistic wage.

Tap into the Soldier for Life Transition Assistance Program (SFL-TAP) at HQDA or at the nearest installation. Especially if you have networked access to no kidding J.O.B.S. https://www.facebook.com/FortCarsonSFLTAP/

In 1992 was passed over to promotion to Major for the second time COL Mikel J. Burroughs. The Army was going through a RIF and the personnel system was trying to reduce the officer corps with as many volunteers as possible an they were offering various buyout plans - a lump sump and and an annuity.
I was a relatively new believer in Christ at the time; but, I was convinced that God did not want me to quit. The previous summer I had interviewed with banking executives in Georgia and I had sent resume's to several other businesses. I did not quit and was forced out of the active component. The next month I accepted a position with a not-for-profit FFRDC company where I was employed for 20 years. I also accepted a commission in the USAR where to my chagrin I was promoted to major based on time in service and grade. By the grace of God I was promoted to LTC just after 2000 after being passed over twice. This allowed me to serve this nation on active duty again soon after 9/11 2001 when I volunteered while my mobilization orders were being processed.
I concur with the comments of COL Jon Thompson.
It is never to early to think about your post-service career. You need to pay attention to the current regulations about what is authorized so that you do not run afoul of current law or regulation; but, putting serious thought into your post-service career and having frank discussions with family and friends is a good idea. Your family and friends may well have a good idea of what you strengths are and if they are true friends they will tell you your strengths and weaknesses.

I will argue that SM need to start thinking about it right away. In 1995, I was passed over for promotion to Major and faced with trying to figure out what I was going to do next. I stretched out my remaining time as long as I could but still left active duty without a job. I never envisioned anything else so I did not have a backup plan. So I say that people should at least have an idea of what they want to do. It may be somewhat easier for officers than a junior enlisted but they should not wait until they know they are leaving. I would say that continued civilian education is also part of this. In terms of actual timelines, the Army has ACAP to help out transitioning Soldiers. Each post should have an ACAP office. Below is the Army site for ACAP and that should be a good starting reference for one who knows they are leaving. I do think that a SM should be serious about it in their last year and they need to find the right balance between their duties and their responsibilities to themselves.
https://www.acap.army.mil/default.aspx