We make the sound in "head" with our mouth open wider than for /i/ or /I/ and our tongues not as close to the top of our mouths.
The sound in "hate" is actually a dipthong, which means it is a combination of the sounds /e/ and /I/. You can feel your tongue moving closer to the roof of your mouth when you say it.
Now let's listen to some sounds!
|"head" sounds:||"hate" sounds:|