How do I know if I have healthy sperm?

Normal Semen Test. A semen analysis evaluates several important aspects of the sperm seen in the ejaculation. The most important are volume of ejaculate, concentration of sperm, % moving, % moving mostly straight, and the appearance of the sperm. If all these are normal, it doesn't always mean "healthy" sperm, as no such term is recognized. Normal semen analysis = fewer fertility issues in the male.
See your doctor. Have a sperm count done to make sure you have adequate numbers and they are "swimming" will need to look at them under a microscope to see this.