Here it is, unfortunatly, I don't think it's in "laymans terms". The first thing is to learn exactly what odds are.
Odds vs Probablility
Odds
-bad:good
Probability
-good in total
total = bad + good
so if my odds are X:Y the probability will be Y in (X+Y)
so 3:1 is the same as 1 in 4
Converting a % to odds
if you have a x% chance of winning your odds are
100-x:x
so if you have a 30% chance a winning the odds are 70:30
70:30 can be simplified to 2.3:1
Converting odds to a %
If your odds are X:Y you will have a [Y/(X+Y)]*100% chance of winning.
How you can actually use this
If the pot is $13 on the river and your oppoent bets $10 how sure do you have to be that you're beat in order to fold?
The odds are 2.3:1 so if you're more than 30% sure you're beat you should fold.
Let's say I'm 40% sure I'm beat and I call. I lose 60% of the time costing me .6*$10 = $6. However I'll win 40% of the time gaining me .6*$23 = $9.2.
How you can apply this to draws
If I have flush draw on the turn with a pot of $20 and an incoming bet of $7 and I want to determine if I have good pot odds I use the same logic as above. There are 46 cards in the deck and 9 are outs so the odds are 37 bad cards. So my odds are 37:9, this is about 4:1. So if the pot is four times the incoming bet I have good pot odds. In this case I'm 4:1 on my draw and 3.9:1 on my draw. So my pot odds are not good. Of course it's still an easy call because pot odds neglect any money I can win on future streets. So as long as I can get him to call a bet of at least $1 on the river when my flush hits I would be correct to call due to
implied odds.
It's all much easier than I made it sound. Just memorize the basic odds below.
Flush--4:1
Open-ended straight--4.5:1
Gutshot straight--10.5:1
Before calling with a draw ask yourself: will I profit at least (appropiate odds based on draw) times the incoming bet?
One more thing to consider, drawing dead. If you've got a gutshot, there are 2

on the board four callers ahead of you it's likely that you have three outs not four...just look for things like that.