Okay so... hmmm how do I start?
Constructed is a format defined by refinement to a known meta-game, where as in limited you are mostly adapting to opportunity and the added variable of probability distribution of cards on top of draw chance. You don't have any meta-defining super threats such as targomoyf, just average level threats across the curve.
- this means that the meta is largely defined by aggro and mid range decks.
- control is not impossible but it is more likely to crop up in sealed where you simply have the cards given to you, rather than trying to create a control deck from the onset in a draft where is is highly unlikely you will get the right tools.
- combo decks are practically impossible. You can work in possible combos as part of your synergy, but basing your deck on a combo going off is a baaaad idea.
- specific meta-cards such as board sweepers are much rarer in limited, which vastly increases the viability of a balls-to-the-wall aggressive mentality. Curving out (1cost critter first turn, 2cost critter second turn etc.) will win a lot of games if the opponent is not so lucky/equipped. Because of this you should try to at least start putting creatures down on second turn. I do not recommend trying to saturate your deck with 1cost critters in order to get the perfect curve, but you need to bare in mind that some people do and they
will stomp you if you don't have some way to control them.
- you can pretty much throw anything that does not directly affect the game state into the unusable pile. Even if you opened a $10 rare, the use of indirect cards is reserved for a refined constructed meta. As a rule you can pretty much ignore counter spells unless you really know what you're doing.
- learn all the viable commons in the set. This includes all removal, all creatures with stats no less than 1/1 below their mana cost (so a 2/2 for 3 would be viable in a pinch), all large creatures or large spells (referred to as 'bombs'), anything that gives or converts mana, and any creature with both an attack stat and some type of evasion. The represent approximately 60-70% of the cards you will face. You also want to be familiar with cards if you are drafting to speed up your decision making.
- card choice priority is usually:
1) quality bombs
2) quality removal
3) quality curve/evasion creatures
3) poor bombs/poor removal
4) poor curve/evasion creatures
5) prioritise cards based on what your deck needs more of.
- This is far from an exact formula, as the quality of cards and compliance with deck plan and playstyle is extremely variable.
- Mana fixing and acceleration priority depends on the current set and your deck plan. When I was playing the set was high on multi-coloured spells so it was not uncommon for mana fixers to be first picked in the absence of an absolutely amazing bomb. If you are going for anything mana-intensive then any spells with double or triple mana costs go down in priority (cryptic command would be nigh unusable in a tri-colour limited deck.
Off the top of my head, a limited deck should look something like:
- 13+creatures
- 16-18 lands (generally 17 I think)
- the rest of your spells should generally be removal or some other board effect.
- there is no real limit to how many creatures you should have, just don't cut land.
- never go over 40 cards. Ever. If you are weak, 41 max.
- note that there is no 4card limit in for decks in limited. If you manage to get 6 of the same really strong card feel free to use all of them.
GETTING BANG FOR BUCK
If you are playing competitive limited it is likely you get to keep at least all the non-rares you pick. Looking up the cost of the rares and uncommons and prioritising accordingly can cover the cost of the draft before taking into account the possibility of winning it. This works particularly well if the card you pick is also good in limited (obviously).
POLITICS
As I mentioned before, this is not my area of expertise. It's not that I am incapable of understanding it, just that I've never really covered it on a theoretical level, and never had it explained to me. The fundamental principle is signalling. You need to send signals to the person 'downstream' from you, so that they will not be taking up the cards you want for your deck. An example of this is forgoing the white serra-angel bomb card for some other option, in order to ensure that the person to your left is going white. You then try and monopolise colours that are not white, preferably the colour that the person to your right is signalling you to go.
There is obviously some elements of luck involved in this process, people who commit to colours that other players are not taking are going to have stronger card pools. It is for this reason that non-committal picks take high priority, an adaptive mind-set is crucial.
Well there's your broad overview, I hope it's not too long
If you require any clarification feel free to ask. Also, these are good rules of thumb for a rookie, but someone who really knows what they're doing could easily break any one of these rules by applying the correct counterbalancing.
so I don't need to stop. But if you get a good group of people and play league style, it doesn't cost a lot of money. 
