There are many ways the parasites can evade the immune-response. It all depends on how it cycles, and if it is intra-cellular or extra-cellular. Size is onother factor, as well as reproduction.
If entering[invading] a cell, for example, it will leave antigens on cell surface at point of entry. It will do the same when exiting. These antigens can be detected by the immune-cells, and may attack that cell. Problem is, if the zygote matures before cell is destroyed, it will have completed it's cycle and there will be a bunch of new parasites available to invade cells. So this can go on forever. Although, once these types of parasites are 'free floating' they are vunerable to attack. Some parasites can protect their receptors with various molecules, or capsules. But they can be vunerable to attack or recognition of "not self" antigens from feeding vacuole or mouth, and excretory areas including reproductive "hole". Larger parasites like worms, are very tough, and although anti-bodies do attach, the "opsonization" process is slow, and sometimes not strong enough to kill 'em. Some have slime-coats which make it extremely difficult for immune-cells to be any good at all.
The important thing is that antigen-presenting cells and effector cells work in harmony with each other. They can take down "big worms" this way by cross-linking receptors and essentially agglutinating the organism and suffocating it.