help me im a noob.

[econ21]

im a new player of this game, i.e. noob.

Try reading frogbeastegg's guide to RTW in the Guides forum. It's very well written and has a wealth of information.

Bear in mind, there are major differences in unit quality within a class. This makes RTW not quite a "rock-paper-scissors" game. For example, Roman equites and Legionary cavalry are both cavalry, but the latter are far superior. The unit stats tell you this, especially the attack stat compared to combined defence (defence skill + armour + shield). For cavalry, the charge stat can be added to the attack stat for the opening part of a proper charge. The purchase price is a reasonable indicator of effectiveness and the stronger units are higher up the tech trees.

cavalry are strong against missile units.

In RTW, cavalry are strong against almost everything (not elephants, I guess). But to be efficient, you have to use them right. This means:
(a) use their mobility to charge into the rear or flanks of already engaged enemies
(b) make sure you get a proper charge off - ie lances levelled. To do this, make sure they have a decent run up before they hit home. Order an attack at the last minute and they'll blunder into melee without a charge bonus.

spearmen are strong against cavalry

Cavalry should avoid charging stationary (braced) spears facing them. But it can be hard in RTW to use spears well against cavalry (too slow and not that deadly to them).

A special kind of spear is the phalanx. While it should be good against cav, in my experience, under human control it excels at grinding down infantry frontally. If the AI has them, strike the phalanx flanks or rear, or shoot it to death.

but i dont know who the missile units, i.e. archers are strong against,

Archers kill anyone, but need protection to do it. Their fire also imposes useful morale penalties, softening up the enemy so they break first in an otherwise fair fight. In this game, the aim is not to kill the enemy where he stands, but to break his morale (where upon you can kill him with cavalry as he routs)

or who are strong against spearmen.

Archers can do it safely, if protected. "Swords" - e.g. legionnaires - are probably supposed to be the anti-spear unit.

also, i dont know how the following units fit in this cycle: heavy infantry, light infantry, missile cavalry, dogs, etc.

Heavy infantry include the swords and armour piercing units like axemen etc. They are good against most spears, good at storming walls etc. Theoretically weak against cavalry, if charged.

I am not sure what light infantry is - maybe you mean javelin armed skirmishers? In RTW, they are like poor man's archers. In some mods like RTR and EB they are great.

Missile cavalry is interesting - it's about as good as foot archers at shooting, but has cavalry's mobility. Probably best to use it to get around the rear of a unit (so they can't use their shields against your arrows). It is often fast enough to outrun most cavalry, so it can be used to disrupt and distract. It needs micromanagement but is arguably the most powerful unit type in a field battle.

Dogs are ahistorical abominations that have no place on a battlefield, sorry going off on a rant. Dogs are like mini-cruise missiles - unleash them on the enemy from a distance and keep the handlers safe so they can rear fresh puppies for the next battle. In that, they are almost like archers - killing from a distance, without losing men themselves. They rip up lightly armoured infantry. They can be countered by heavy cavalry (esp. generals' bodyguards which are totally uber in RTW).

[Fwapper]

If you haven't already - play the prologue up to the first battle (not very far) it gives a basic taste of battle tactics. Also (and this one can be hard) pay attention to the advisor. And finally, just always try to pin an enemy unit with one of your units, then charge into it's rear or side with another of your units (cav are best of this.)

Hope that helped, Fwapper.