You'll have to dig around till you find it.
Just dig exploratory shafts all over the place.
There is actually a better way than "dig and hope for the best" - there can be a science to it.
If you were wise, you noted in your Embark map where it was - that's your first big hint.
(Copied from a question about "How to find a magma pipe", but it goes on to address this question...)A magma pipe/pool is about 20-25 tiles across (which is big!), a rough circle, and rarely more than 6 deep from the surface. (Obsidian ovals or sheer edges can be a giveaway.) Each is entirely enclosed within it's own area tile - one of the symbols you saw in the Local map at Embark. Each of those is 48 individual tiles square in your game map (tho' you could call it 50 and be close - <Enter+ direction key> = a jump of 10 tiles). You can find them by counting from a corner, and you'll often see the stone/flora change at that cutpoint. Digging down in the dead center of each 48x48 area tile usually* finds any pipe/pool - and underground pools are even bigger. (* There's a small chance you'll just miss it - then go about 12 tiles out in 4 directions, either all orthagonal or diagonal, and try again.)
If you're randomly mining a pattern of shafts, you could do it in a grid about 20 apart. If you noted where the magma was on your embark map (hardly cheating), you have a perfect idea of where to start looking.
UG Rivers are harder to find - they're more narrow, and far deeper. They often run orthogonally or perfectly diagonally, but not always. I'd plan to run a 6x6 grid of deep shafts, but start off with a staggered grid at 12x12. (A 6x6 grid can be filled in to become 3x3 if you want to do perfect exploratory mining at 100% later.)
If I know where the UG river is from the embark map, I'll dig a row of 4 exploratory shafts, 12 tiles apart, across that area block. If those miss, I fill those in at 6 tiles apart - the odds are ~almost~ 100% that I'll hit it with those 7 shafts.