Science vessels are the mobile detectors of the Terran army. They come very late in the game, making a Terran play rely on comstat and turrets for detection. This forces the Terran to be very defensive. The science vessel is very powerful against all races. They have 3 great spells, defensive matrix, irradiate, and EMP shockwave.
Defensive matrix will give a unit +250 HP and that unit will take 1 point of damage from any attack. Basically make any unit into a super unit for a limited time, to absorb damage. Since the AI will make units attack the unit that does the most damage, use defensive matrix on battlecruisers, tanks, and goliaths. There are a few uses for defensive matrix. Use it to give a ghost the extra time he needs to complete the nuclear drop. Be warned, if you defensive matrix a cloaked unit, he is no longer invisible. Also try casting defensive matrix on all of your dropships, making it possible to drop on those heavily fortified islands.
Irradiate is one of the best spells in the game. Since you gain the mobility of the science vessel, it maks it easier to select your targets. It is almost comparable to psionic storm, since it will kill an organic unit of your choice.
Cast irradiate on expensive units, as templars, queens, lurkers, dark templars, and defilers. It will kill that unit, if no medic is around to cast restoration. Try not to use it on mass units, since the effect isn't as strong as psionic storm, and the effect will last as long as the unit stays alive. Casting on units that are immune to irradiate will give them an added attack. For example cast it on tanks to protect them from melee attackers, or vultures to run into mineral lines and kill off workers.
EMP shockwave is also a powerful spell. It will drain the shields of all Protoss units caught in the blast. It will also deplete any mana or energy that a spell caster has. There aren't too many tricks to use EMP shockwave. Try casting it on mass range units since they tend to be stationary and bunch up.
Dragoons, corsairs, scouts, and carriers are good targets. Try to force a Protoss player to bunch his templars up in the middle of his base by using irradiate. Since if the Protoss player lef this templars around the outside of base, you can easily pick them off with irradiate and yamato gun. Try to defenesive matrix a science vessel and sacrifice it to EMP shockwave all his templars, which is far more useful than casting irradiate. Using EMP on wraiths is also powerful, since it will take away any cloaking ability. Also casting EMP on groups of battle cruisers is good to get rid of any yamato guns. EMPing Protoss strucutures will make it possible to destroy them with one nuke.
Science vessels are expensive, and shouldn't be left to die. Repair them once they take damage.
