What was going on when I was born?

The $9 million in state money needed to avert a threatened layoff of 1,000 New York City teachers will be provided, Governor Cuomo said yesterday. The state agreement was the final piece of a $40 million package that included some cuts by the school board and money from City Hall. It was reached after a series of telephone conversations and negotiations between officials in New York City, Albany and around the state. ''We got a deal,'' Timothy Russert, the Governor's spokesman, said in early evening.

The Government's index of leading economic indicators, intended to forecast economic trends, rose 1.5 percent in December, the largest increase in the past two years, the Commerce Department reported today. It was the eighth increase in nine months. But the December rise was much more broadly based than the previous months' gains and was seen by some Government economists as another of several recent signals that a recovery from the recession is finally at hand. In addition, a companion index that measures the current state of the economy fell only one-tenth of 1 percent last month, the smallest decline in the past year. That measurement, the index of coincident indicators, which measures changes in personal income, industrial production, employment, and manufacturing and trade sales, fell a slight two-tenths of 1 percent in November.

President Reagan is proposing an $848.5 billion budget for the fiscal year 1984 that keeps pace with expected inflation and projects a deficit of $189 billion, provided Congress enacts a series of freezes and reductions in domestic programs. The budget assumes that the nation's economic recovery is under way in the current quarter and that it will build steadily until midyear and then average 4 percent growth for the next five years. It predicts that unemployment will peak in the first half of this year, with the economy producing 1.6 million new jobs by fall and 4.6 million more by late 1984. Against this backdrop, the President proposes an increase of $43.5 billion in overall Federal spending from 1983, with $30 billion of that increase going to the Defense Department. Military spending would rise from $208.9 billion this year to $238.6 billion in the fiscal year 1984, which begins next Oct. 1.

A car packed with explosives blew up today in eastern Lebanon outside a building belonging to Yasir Arafat's Al Fatah Palestinian guerrilla group, killing 14 people, the state-run Beirut television said. According to security sources, the three-story building near the town of Shtaura was used as an office by Al Fatah's military intelligence branch -known as ''17'' - which is under the direct control of Mr. Arafat, the Palestine Liberation Organization chairman. In phone calls to the offices of Beirut news organizations, a group calling itself the Front to Liberate Lebanon From Foreigners said it was responsible for the attack. The group has repeatedly taken responsibility for attacks on Palestinian targets in the last two years.

Republican and Democratic Congressional leaders today fastened on a single word, ''realistic,'' to describe the economic underpinning of President Reagan's budget for the fiscal year 1984. The leaders said there would be battles ahead but that White House officials had indicated a willingness to work out budget differences with Congress. The Congressional reaction contrasted sharply with that of last year, when the President's budget was quickly discarded on Capitol Hill. Today's reaction suggested that Mr. Reagan's budget had been designed with the active participation of Congressional leaders. 4% Growth Rate Projected The budget projects an annual growth rate of 4 percent in the gross national product, an inflation rate of 4.4 percent, an interest rate of 7.8 percent on 90-day Treasury bills and an unemployment rate of 9.5 percent.

Governor Cuomo will seek a 36 percent increase in unemployment benefits, from $125 to $170 a week. Page 25. By JOSH BARBANEL Tuition at the State and City University systems will rise sharply under the proposed state budget, and layoffs and cuts in purchases will be required, aides to Governor Cuomo said yesterday. In the next academic year, tuition for students in the 34 four-year colleges of the State University system would rise by $250, to $1,300 a year, and dormitory fees would go up by $150, to $1,400 a year, according to the Governor's staff. Current enrollment is 193,000.