On Wednesday Congress will begin the tortuous, contentious process of recasting President Reagan's $848.5 billion budget into its own spending and tax decisions for the 1984 fiscal year, starting Sept. 30.

Its task will be complicated by continuing disputes over how to handle the budget. There could be changes in the nearly 10-year-old congressional budget control process, and in any case there will be efforts to manipulate that process toward various political and economic policy goals.

The focal points will be the budget committees of the two houses, which have existed only since 1974 but in the Reagan era have emerged as powerful forces that in effect set the agenda for most other committees by setting general tax and spending targets.

This power has prompted proposals in both houses for curbing the budget committees, openly among House Democrats and more privately among Senate Republican leaders. And these proposals will be considered even as the two houses are also working on the budget.

The Senate Budget Committee will remain basically the same as it was during the first two years of the Reagan administration, with Sen. Pete V. Domenici (R-N.M.) continuing as chairman and as a central, outspoken figure in the efforts of Senate Republicans to reshape Reagan's budget to make it palatable to Congress.

Democratic leadership on the panel remains in moderately conservative southern Democratic hands as Sen. Lawton Chiles (D-Fla.) replaces Sen. Ernest F. Hollings (D-S.C.) as ranking minority member. Domenici and Chiles are expected to work closely.

The House Budget Committee will continue to be chaired by Oklahoma Rep. James R. Jones, another right-of-center Democrat. But new appointments to the committee in the wake of Democratic gains in the November elections point to a more liberal, traditionally Democratic outlook for the committee, where ranking Republican Delbert L. Latta of Ohio and other GOP members--probably including Phil Gramm, the Texas Democrat who resigned to seek reelection as a Republican --will probably find themselves with less maneuvering room than before.

Although Jones talks of a "bipartisan" approach, other Democrats have made it clear they want what they call a "real Democratic budget." And, with the Democratic gains in the House, Reagan's highly successful bipartisan budget coalition of the last two years does not appear to have the votes to prevent passage of a Democratic budget this year.

Nonetheless, there is talk among senior members of both parties, including House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) and Senate Majority Leader Howard H. Baker Jr. (R-Tenn.), of joint initiatives to avoid what some lawmakers fear could otherwise be legislative paralysis on budget-related issues like jobs-creating programs.

Both of the budget committees will begin hearings Wednesday, starting off with top economic policy makers from the administration. After several weeks of hearings, the panels will begin drafting their versions of the Reagan budget, which was rejected out-of-hand last year but is expected to be used at least as "the point of departure," as Baker put it, in drafting the congressional budget resolution this year.

The committee-approved budget drafts will then go to the floor of both houses, and a final version will be negotiated in a House-Senate conference, subject to approval of the two houses.

Presidential approval is not required, because the budget is only a fiscal tool for Congress, not a law.

In theory, the first budget resolution sets only targets for spending and taxes. But last year Congress, weary of fighting budget battles twice, automatically converted the targets to binding ceilings in September, when it was theoretically supposed to pass a second budget resolution. The process may be repeated this year.

But even then the budget is only a blueprint, with limits on broad categories of spending that can be broken by a majority vote of the two houses. Real decisions are made in the fine print of subsequent authorizing and appropriations bills.

In the first two years of Reagan's administration, deficit reductions were made in so-called "reconciliation" legislation, in which the two houses ordered committees to make program cuts to bring spending in line with budget targets.

The committees have complained that the "reconciliation" process eroded their powers. Whether it will be used again is unclear, although it may be harder for Reagan to achieve his spending cutbacks if the process is abandoned.