For most taxpayers the first impact of the $98.3 billion tax increase bill approved by Congress Thursday will come on Sept. 1. That day the tax on domestic airline tickets is to go from 5 to 8 percent.

On Jan. 1 the cigarette tax will rise from 8 to 16 cents a pack, the tax on telephone service will go up from 1 to 3 percent and the government will start withholding the 1.3 percent Medicare tax from federal workers' paychecks.

But the most controversial part of the new law as it affects individuals will not take effect until next July. That is the provision requiring banks, savings and loans and other payers to start withholding taxes from interest and dividend payments just as they are now withheld from wages. The withholding rate will be 10 percent.

The cigarette and telephone tax increases are expected to be passed along to consumers. In many states, cigarette prices will go up more than 8 cents because state sales taxes are added on top of the federal excise tax. These increases could push retail prices near $1 a pack.

Airline industry officials said the additional 3 percent tax probably will be added to the price of tickets, but each airline has the option of absorbing some or all of the cost for competitive reasons.

The fare on the popular Eastern Airlines Washington-New York shuttle, for example, is $60, so the tax will increase by $1.80. A spokesman for the airline said it had not decided whether to raise the shuttle fare, but on longer flights, he said, the increase will be passed on because "We fly about 35 million people a year, and if we absorb even $1 per ticket, that's quite a chunk of cash."

Also on Sept. 1, a $3 tax on each passenger boarding international flights, a tax in effect throughout the 1970s, will be reinstated.

Federal workers will become automatically eligible for Medicare in turn for paying the Medicare tax. The 1.3 percent will apply next year to the first $35,100 of wages, for a maximum tax of just over $456. About 345,000 civilian federal employes in the Washington area will be affected.

Taxpayers who itemize their deductions will be affected by a provision of the bill affecting medical expenses. This will take effect Jan. 1 and apply to taxes on 1983 income; it will not actually be felt by most taxpayers until they pay their 1983 taxes in April, 1984.

The tax bill eliminates the current deduction of up to $150 for one half of health insurance premiums paid. It also limits medical deductions to those costs in excess of 5 percent of adjusted gross income, instead of 3 percent as now.

There are exceptions to the interest and dividend withholding provision.

Any savings or other account paying interest of less than $150 a year may be exempted at the option of the paying institution; there is no similar exemption for dividends.

Persons over 65 who paid income tax of $1,500 or less the year before -- $2,000 on a joint return -- or those under 65 who paid $600 or less -- $1,000 on a joint return-may exempt themselves from the withholding requirement, but they must fill out separate applications for each bank account, certificate of deposit, or other source of income.

This will be the first time such a provision has been in effect in this country, and the financial institutions say they expect a bookkeeping nightmare as they try to comply.

In fact, the Senate and House conferees who worked out the final details of the tax bill last weekend anticipated such difficulties, and authorized the banks and other affected institutions to hold on to withheld tax funds for 30 days to compensate them for the cost of setting up the system.

"The conferees realize," they said in their report, "that although many elderly and low-income persons will qualify for exemption, they will need to file exemption certificates to enjoy the benefit of their exemptions. In addition, the withholding rules will affect the financial planning of nonexempt individuals.

"Therefore the conferees anticipate that the Secretary of the Treasury will endeavor to inform the public about the operation of the withholding rules and the requirement that exempt individuals file exemption certificates . . . . The Internal Revenue Service should notify and counsel affected individuals through new or existing taxpayer-assistance mechanisms and should create forms that are as simple to understand as possible."

In theory, the withholding measure does not increase the tax liability of investors, but only guarantees that Uncle Sam will get what is owed, and get it sooner. However, it could reduce income from investments on which interest is compounded.

An analysis published by Prentice-Hall Inc. gives the example of "a $10,000, 10 percent bond, under which interest is compounded quarterly and rolled back into the investment. Under the new rules, 10 percent (or $25) of the $250 March 31 interest payment is withheld and deducted. As a result, the June 30th interest payment will be based on 2 1/2 percent of $10,225, not $10,250. After a few years, the lost interest can add up."