An EKG has several waves that are correlated with different components of cardiac depolarization (heart beats). First is the P-wave. Then 3 waves one right after the other Q, R, and S. Then a T-wave. The spaces in between waves where the tracing returns to baseline and is flat are called segments.
If the segment between the S-wave and T-wave is elevated above baseline in a charecteristic way it is indicative of a heart attack and we call it a STEMI (ST Elevation Myocardial Infarction). If the patient is having a heart attack even though we don't see any elevation in the ST segment, its called an NSTEMI (Non ST Elevation Myocardial Infarction.
So you check for it on the EKG. When you have a slam dunk STEMI you go to the cath lab and they take pictures and hopefully find the blockage and then you know. If its an NSTEMI you do blood work to look for evidence of a dying heart muscle, then you know.
Sometimes people have ST elevation with out a heart attack, sometimes they have a heart attack without ST elevation. Sometimes they have a "heart attack" but don't have a blockage. Sometimes they have a blockage but don't have a heart attack. Basically, as EMS you don't always know, and neither does the ED, and neither does the cardiologist until they go in and look. But a STEMI on EKG is a pretty good bet that the heart is dying.