When playing swing eighth notes, it is easier to count them as eighth notes rather than triplet subdivisions, i.e., count them 1 and 2 and 3 and 4 and, with each "and" being half as long as the note on the beat. Try playing through the scale from C to C ascending, D to D descending, E to E ascending, etc. Using swing eighth notes as shown in the following example and count as you play.
Once you start to feel comfortable using swing eighth notes, try improvising with them. Start with some set rhythms by adding rests or other note values. The following example uses a rest on the first beat of the bar.