My client is 100% owner of S-corp in PA. effective 1-1-18 he transferred 49% to his son for $10.company has been valued at $3M.where and how do i report such transaction?

"please help me understand the basis vs equity difference. their books are kept as tax books. before the transfer, Father's basis was initial Capital Stock of $100 plus all net profits (or losses) from the date of incorporation, plus Additional Paid-In Capital, less non-deductible items (charity, section 179, life insurance premiums, 50% meals etc), less distributions. so at any given moment i could say Father's basis is equal to Total Equity on S-Corp Balance Sheet. is that correct?"

Nothing changed for the Corporation. You are confusing the number of shareholders and their proportional split, with the Corporation's financial perspective. You only changed Number of Shareholders and now there is a Split for purposes of the K-1. Let's try this example, Olga:

If I own 5 shares of Ford Stock, the Ford bookkeeping doesn't reflect my personal ownership, because it doesn't affect Ford Corp's financial position. If I decide to sell those 5 shares to you, or only 3 of them, nothing changed for Ford's financial perspective and they do not put this into their financial records. That's why nothing about that $10, or basis or equity, has changed for the corporate books.

Olga asked: "what should they have done differently?"

Ownership has changed, for purposes of the tax reporting to the Shareholders, on the K-1, and one shareholder just Sold some of their shares. But unfortunately, by gifting 49%, the father bypassed what could have been a Step Up in basis. If the father had put the shares into a will or trust as transferring to the son on death, the Son would get that basis as of the date of Death. See how that is a better financial transaction for both parties?

"where do you guys learn all this?"

I'm not a CPA; I lurk here and learn from the others. I consult with small businesses and other entities, and I teach QuickBooks, which means I need to understand how these things should be tracked, which means I need to understand what is done from the beginning and what are the options and impacts and considerations. One of the CPAs here is better able to address hypothetical basis and gain as per your examples.

As for this (instead of an outright sale to start with): "What would Son's basis be in a year or two should he decide to sell his shares?"

From the perspective of what they actually did, you have the answer right in your topic, above, which is why I read these topics and how I learn about these subjects:
Son's basis in stock = 49% of father's basis immediately before transaction. <== sjrcpa

Because that is a gift of Basis minus $10. Again, as provided by sjrcpa:
The gift is FMV less $10. Son's initial basis in the stock is $10 + 49% of father's basis.

Because of the way they did this activity.

"it was not in any of my textbooks..."

"was" never matters. Textbooks are not a useful reference, after printing date. "Now" is what matters. You know the tax regulations changed with the Dec 2017 TCJA, and they often are changed. You have to stay current in your field. People are relying on your guidance and your tasks affect them.