December 31, 2012
Assets	$	55,000		$	34,000		$	24,000		$	60,000		$	119,000
Liabilities		24,500			21,500			9,000			40,000			?
December 31, 2013
Assets		58,000			40,000			?			85,000			113,000
Liabilities		?			26,500			29,000			24,000			70,000
During year 2013
Stock issuances		6,000			1,400			9,750			?			6,500
Net income (loss)		8,500			?			8,000			14,000			20,000
Cash dividends		3,500			2,000			5,875			0			11,000

How do I find net income in the second column of this sheet?

For this type of problem you need to know 2 formulas; 1: basic accounting equation, and 2: changes in equity.

The basic accounting equation is:
Assets = Liabilities + Owners Equity which can be rewritten two additional ways to find a missing amount. The other ways it can be written are:
Liabilities = Assets - Owners Equity
Owners Equity = Assets - Liabilities

Now for changes in Equity the expanded formula is:
Ending Owners Equity = Beginning Owners Equity + Stock Issuances(additional investments) + Net Income(Revenues - Expenses) - Cash dividends(or drawings)

For Net Income the formula can be rewritten as:
Net Income = Ending Owners Equity - Beginning Owners Equity - Stock Issuances + Cash Dividends

For Stock Issuances the formula can be rewritten as:
Stock Issuances = Ending Owners Equity - Beginning Owners Equity - Net Income + Cash Dividends

To Find assets use the beginning owners equity and solve for the ending equity, then add your ending owners equity and ending liabilities.