The purpose of a consistency tree is to test whether it is possible for the premises in an argument to be true at the same time that the conclusion is false.  If they can, we say they are consistent, but this means that the argument is not pattern perfect (deductively valid).

Let's say we have the premises of P->Q and P, and the intended conclusion is Q.  We line up the premises along with the negated conclusion:
P -> Q
P
~Q

What we now want to do is break down any expression with more than one term.  When we have something like P & Q we would just write P and Q over each other in a line.  When we have P v Q we branch out.  With P -> Q (which you should now recognize as equivalent to ~P v Q) we again branch out, but we negate the antecedent.
P -> Q
P
~Q
/  \
~P Q
Now let's look up each branch.  We see that ~P contradicts P at the same time that Q contradicts ~Q.  This closes each branch, and we mark this with an "x."  Since we have no open branches (meaning it is inconsistent to have these premises true together with this conclusion false ) we can say that the argument is valid.
P -> Q
P
~Q
/  \
~P Q
x  x
valid
But let's look at a different argument: P->Q, Q |- P
P -> Q
Q
~P
/  \
~P  Q
invalid
In this situation we still have open branches, meaning that it is consistent to have these premises true while the conlusion is false, and that is what we define as an invalid argument.

Some FAQs:

Can a tree be set up in more than one way?
Yes, indeed.  The easiest, though, is to work through the premises to have as few branches as possible.  Let's say we have this argument to test:
(P & Q) -> R, S -> ~R, S & Q |- ~P
We always set up the tree in the same way for the premises and the negated conclusion, but look at two different ways we can then go on.
(P & Q) -> R
S -> ~R
S & Q
~~P
S
Q
/  \
~S  ~R
x   /  \
~(P&Q)  R
/  \          x
~P ~Q             
x   x           
valid

(P & Q) -> R
S -> ~R
S & Q
~~P
/      \
~(P & Q)  R
/   \           /  \
~P ~Q    ~S  ~R
   x     S      S     x
   Q      Q
   x         x
valid
They both lead to the same result, but the second is a bit more complicated.   (In this example, did you note how DeMorgan's Law comes into play in breaking down the first premise?  Make sure you review the decomposition patterns in chapter 14.)

When should we use trees rather than truth tables?
Some students find the reverse method easier with propositional expressions (those without quantifiers), others find the trees easier.  They both play off the same idea of it being inconsistent to have true premises and a false conclusion when an argument is valid.  However, once we begin working with quantifiers the trees have a definite advantage.