There are two ways to pay tax on the assets placed in a trust fund. With a revocable trust, the grantor -- the trust creator -- owns the income from the trust assets and has to pay the taxman. If the grantor sets up an irrevocable trust, the assets no longer belong to her, so the trust pays its own tax. When beneficiaries start taking money out, it's their turn to pay the IRS.
Any money you withdraw from a trust fund -- which is just a term for the assets and money in the trust -- is taxable income. You pay tax the same way you would if the trust assets belonged to you. If you receive income from stock dividends, you report dividend income; if it's rental property, you report it as rental income, and so on. Unlike a case in which the assets are your own, however, you can't take a write-off for the trust's losses.
Your taxable income for this year includes everything the trust gave you, and any money it owes you but hasn't paid you yet. This can happen if the trust generates income due to you in, say, December, but doesn't pay out until January. It could also happen if there's a question about who should get the money and the trustee doesn't have an answer. If the money is due to you this year, it's taxable income even if the trustee hasn't cut you the check.
What's taxable to you is actually a tax break for the trust. To prevent double-taxation -- the trust paying tax on its income, then you paying tax on the same money when you withdraw it -- the trust gets a write-off for what it gives you over the course of the year. If the trust's distributable net Income is less than it pays you -- this could happen if, for instance, you tap the trust principal -- the tax deduction is limited to the DNI.
You don't have to go over the trust accounts to figure your taxes out. The trustee has an obligation to tell you what sort of income -- dividend, interest, royalty and so on -- you receive during the year. If the trust income triggers a 1099 form, you should get one in the mail just as if you owned the assets. When the trust pays you more than $10 in dividend income, for example, you get a 1099-DIV.