Skyrocketing costs have virtually pushed tuition and other college-related expenses beyond the savings and income of the average family.

In fact, unprecedented increases in tuition at public and private colleges and universities have outstripped the savings of many of those who started a college fund when their children were very young.

The average annual cost of attending a state-supported, four-year school has risen close to $5,000. For private institutions the figure is nearly $8,000.

But with careful planning and resourcefulness, parents of academically qualified students can fulfill the dream of sending their childern to college.

Above all, planning to pay for a college education should begin early. In the case of families whose children expect to enroll in college next fall, however, it is still not too late to find a way to finance college expenses, either by borrowing at favorable rates or by obtaining scholarship aid or direct grants.

Costs are expected to increase 10 percent or more next year. And rising costs coupled with confusion over cutbacks in federal student aid have prompted many families to give up all attempts to finance higher education costs.

But the effects of those cutbacks aren't as serious as they might have been. Moreover, financial aid is available from hundreds of sources, and with patient research parents and students can often tap one or more of them for funds necessary to pay for a college education.

Ideally, parents should start building a college fund when their children are in elementary school, if not sooner. But given today's costs, loans and scholarship aid are in great demand by many families who began planning early for expenses.

For families with income levels high enough to finance a college education without outside help, establishing trusts at financial institutions is a proven way of building a college fund.

Trusts can be devised in several ways and tailored to meet the individual family's needs. For tax purposes, it is generally advantageous to transfer funds from the parents' accounts to a child's trust.

One of the least complicated ways of saving for college is to establish a savings account in a child's name. Money saved through a child's account will not be taxed as heavily as that in a similar account held by his or her parents. In fact, the initial $1,000 of interest earned on a child's savings account will be free of taxes. After that taxes are at least 12 percent.

The child's money may be invested in certificates or in a money fund or some other instrument.

Colleges expect students and their families to accept financial responsibility by contributing to college costs. The size of the contribution will depend on the family's income, assets, size, number of children in college and special financial circumstances.

The exact amount of the contribution is determined by a formula used in a "needs" analysis. For example, a family of four with one child in college, a pretax income of $32,000 and net assets of $40,000 will be expected to contribute about one-tenth of income before taxes to college costs.

Families with adjusted gross incomes under $30,000 do not have to pass a "needs" test. And families with higher incomes may be able to obtain aid if they meet certain criteria.

Sources of financial aid are numerous and include community organizations, special state funds, employers and the federal government. One of the principal sources of information, however, is each college or university's office of student financial aid.

Some of the better-known student assistance programs include the following:

* Guaranteed Student Loans provide low-interest funds insured either by the federal government or a guarantee agency, such as the Higher Education Assistance Foundation in the District. Undergraduates may borrow up to $2,500 a year and have until six months after graduation to begin repayment. These loans may be obtained from banks, savings and loan associations or credit unions at 9 percent.

* The Pell Grant program is the largest of the federal student aid programs. Pell Grants are awarded by the Department of Education based on a standard formula used to determine financial aid. Unlike loans, grants do not have to be repaid.

* The National Direct Student Loan Program provides low-interest loans through financial aid offices at colleges and universities. Students may borrow up to $3,000 if they are enrolled in a vocational program or if they have completed two years of a program leading to a bachelor's degree.

* PLUS loans are among the newer sources of aid. They are available to all borrowers, regardless of income. Parents may borrow a maximum $3,000 annually for each student and $15,000 in the aggregate. Many banks, savings and loan associations and credit unions participate in the program. Repayment of the five-to-10-year PLUS loans, which are made at 12 percent, begins within 60 days of disbursement. CAPTION: Picture, The average annual cost of attending a private college has risen to $8,000.