X-Wing is the first technique that spans four cells in four different units at once. It looks intimidating written down and is surprisingly easy to spot on a grid, because it has a shape.
Find a digit — call it 5 — and two rows in which 5 has exactly two possible cells. If those two cells sit in the same pair of columns in both rows, you have an X-Wing.
Take the four corners of the rectangle. Each of the two rows must contain a 5, and in each row the 5 is at one end or the other. That gives two possible arrangements: the two 5s sit on one diagonal of the rectangle, or on the other.
Either way — and this is the whole argument — each of the two columns ends up with exactly one 5, and it's at a corner of the rectangle. The columns are satisfied. So no other cell in either column can hold a 5, and every 5 elsewhere in those two columns can be struck out.
You never learn which diagonal is correct. You don't need to. Both possibilities produce the same eliminations, which is what makes the deduction valid.
The pattern works in either orientation. Two columns that confine a digit to the same two rows let you clear that digit from the rest of those two rows. When hunting, check both directions — many players only ever scan rows and miss half the X-Wings on a board.
The search is systematic rather than intuitive:
In practice you'll do this for one or two digits, not all nine — you reach for X-Wing when a specific digit is clearly the blockage, not as a routine sweep.
Swordfish is the same argument stretched to three rows and three columns. Three rows each confine a digit to cells within the same three columns, so those three columns are satisfied by the three rows, and the digit clears from the rest of those columns.
The important difference from X-Wing: the rows don't each need exactly two candidates. Two or three is fine, and the cells don't have to line up into a neat grid. What matters is that the union of columns used across the three rows contains exactly three columns. A row with candidates in columns 2 and 7, another in 2 and 4, and a third in 4 and 7 is a valid Swordfish — union is {2, 4, 7}, three columns, three rows.
That looseness is why Swordfish is genuinely hard to see by eye. It's a legitimate technique and it appears in Expert puzzles, but if you're hunting one manually the honest advice is to check every simpler technique twice first. Swordfish is rarely the only route through a grid.
You should not be reaching for X-Wing often. On this site, Easy and Medium puzzles never require it, Hard puzzles almost never do, and Expert puzzles occasionally do. If you find yourself hunting X-Wings on a Medium board, there's a hidden single or a pointing pair you've walked past — go back and check singles, pairs and locked candidates before spending ten minutes on a rectangle.
And as always: one X-Wing elimination rarely finishes anything by itself. It removes a candidate, the removal creates a single, and the grid unwinds from there.