Social Security taxes go up again today, while income taxes come down, but most Americans will not feel the income tax cuts for another six months, and some not until 1983.

The income tax cuts are the second installment of the tax reduction bill President Reagan pushed through Congress last summer, the largest tax cut in history. But for many Americans, particularly those in lower income brackets, they will not be enough to offset the Social Security increase and the effect of inflation, which raises wages and moves people into higher tax brackets.

Under legislation passed several years ago, the Social Security tax rate will rise from 1981's 6.65 percent to 6.7 percent for both employes and employers beginning today.

The Social Security wage base--the amount of an individual's earnings to which the tax applies--also will rise, from 1981's $29,700 to $32,400 this year. The wage base goes up automatically each year the same percentage as wages in the economy generally.

The two changes together mean the maximum Social Security tax will rise $195.75, or almost 10 percent, from 1981's $1,975.05 to $2,170.80 in 1982. As to income taxes, rates in all brackets, which were cut 5 percent Oct. 1, will be cut a further 10 percent July 1. Withholding rates will be adjusted accordingly, but that will not be until summer.

There are also various specialized tax cuts taking effect today. Taxpayers can put more money aside in Individual Retirement Accounts, or IRAs, beginning this year, and taxpayers who are enrolled in pension funds can set up IRAs for the first time.

The so-called marriage penalty, which causes two persons who work to pay more in taxes if married than if they remained single, has been reduced. The child care credit has been increased, and estate and gift taxes have been reduced; for most Americans they will be phased out over the next several years. While Social Security taxes are going up, benefits are being cut. Beginning today, people becoming eligible for Social Security no longer will be entitled to a minimum benefit of $122 a month. Some will get less if their earnings were low in the years they worked. This change is expected to affect 100,000 people this year and save the government $50 million.

For those Americans who can afford to take advantage of it, one of the most significant new tax breaks will be the opportunity to open an Individual Retirement Account, with taxes on the deposited money deferred until the time of retirement. This will encourage an estimated 40 million workers who are already covered by company pension plans to set up additional retirement funds of their own.

Under the new law, each worker can deposit up to $2,000 a year in a financial institution and pay no tax on the deposits or interest until retirement. A person with an unemployed spouse also may deposit $250 in an IRA for the spouse.

Similar changes are taking effect in retirement provisions for self-employed workers.

Until now, tax-deferred IRAs have been available only to workers who are not covered by a company pension plan, and annual deposits have been limited to $1,500 plus $250 for a non-working spouse.

Up to 17 million families in which both spouses are employed will qualify for a new deduction to offset a portion of the "marriage penalty."

For 1982 income, a working couple filing a joint return will be able to exempt from taxes 5 percent of the first $30,000 earned by the lower-earning spouse. That provides a maximum deduction of $1,500. For income earned in 1983 and later the deduction will be 10 percent of the first $30,000, or a maximum of $3,000.

The marriage-penalty deduction also will be available to couples who do not itemize deductions.

On child care, families with incomes under $10,000 may take a tax credit equal to 30 percent of the first $2,400 of such expenses for one child or of the first $4,800 for two or more. The credit phases down as income increases, to 20 percent for those with incomes of $30,000 or more.

Some other major changes in the tax laws:

There have been substantial changes in the estate and gift tax laws, with the first phase starting today. In 1981 the first $175,625 of an estate was exempt from taxes. This year the amount has been increased to $225,000, and by 1986 estates worth up to $600,000 can be transferred tax free.

Americans working abroad can exclude up to $75,000 a year in income, as well as certain housing expenses, from taxes this year.

The maximum tax rate on investment income has been reduced to 50 percent. Although the top rate on wages and similar "earned" income has been 50 percent for several years, interest, dividends and other "unearned" income have been taxed at up to 70 percent.

The tax exemption of up to $200 a year ($400 for a couple) in interest and dividends received has been eliminated. It was replaced by a $100 exclusion ($200 for a couple) for dividends only. Interest from special "All Savers" accounts can be deducted, however.

Taxpayers who don't itemize may deduct a portion of their charitable contributions. This year the provision allows a maximum $25 deduction, but the amount will increase until all limits will be removed in 1986.

Sick pay will be taxable.

Meanwhile, the minimum wage will stay the same, $3.35 an hour, but it will apply to more employes.