I have three chapters covering writing Crystal Reports formulas. I also cover Crystal Syntax and Basic Syntax. Check out chapter 5-7 and Appendix B in my book Crystal Reports Encyclopedia.

Re your question, this actually looks fine upon inspection and I can't say why it doesn't work. You could also try using the IN operator for ranges.

if {leads.created_at} IN {@date_from} _TO_ {@Date_To} Then...

Notice that I use underscores around the TO operator. This means to NOT iinclude the beginning and ending dates as part of the range (similar to '>' and '<'). If you wanted to include the dates as part of the range, then drop the underscores (i.e. just use 'TO').
If this still doesn't work, then something else is causing you problems. The most common cause is that you have a null value in the date field. Set the Report Option to Convert Nulls to Default Values and see if this helps.
If this still causes you problems, then I would debug it by first determining why the If statement isn't working. I would create a formula that just returns the result of the If statement and print that in the Details section. I do that because then I can just focus on the If statement and tweak it until it returns True and False on the records I expect it to. After I get that working then I add the rest of the formula which would do the Sum() functions.

This is an extremely common problem in Crystal.  The basic issue is that your If..Then structure is outside your Sum function.  Hence, Crystal is still taking the sum of all the records.

The simplest solution is to create a new formula, applied to each record.  It would look something like:

if {leads.created_at} >{?date_from} and {leads.created_at} <{?date_to} then

{leads.cost} + {leads.affiliate_bounty}

else

0

Then, you can simply take the Sum of that formula.  This should give you the kind of result you are looking for.

Again, Sum only works on a single field.  You can't take a Sum (or any other aggregate) of an expression.

The simplest solution is to create a formula that does the math for each record, then do a Sum on that.  (As an important caveat, depending on exactly what your formula is doing, you may not be able to perform a Sum on it.)  This is what I did above.  While it looks counter-intuitive, it really is the cleanest way in Crystal.  Note that you don't actually have to put the formula itself on the report anywhere.  Crystal doesn't make you "show your work." 

So, create three formulas:

@Zero_Lead

IF {leads.leaddate} IN {?Date_From} TO {?Date_To} AND
     {leads.leadvalue} = 0 THEN 1
ELSE 0

@Paid_Lead

IF {leads.leaddate} IN {?Date_From} TO {?Date_To} AND

     {leads.leadvalue} > 0 THEN 1

ELSE 0

@Lead_Cost

IF {leads.leaddate} IN {?Date_From} TO {?Date_To}
THEN {leads.affiliate_bounty} +  {leads.cost}

ELSE 0

In your Report Footer (assuming that's where you want it), your fields would look like:

Date_From      Date_To       Zero_Leads           Paid_Leads        Total_Cost
--------------|-------------|--------------------|-----------------|----------
{?Date_From}   {?Date_To}    SUM({@Zero_Lead})    SUM({@Paid_Lead}) SUM({@Lead_Cost})

Hopefully that's a little clearer.

Incidentally, if you are grouping your report by month, rather than entering your beginning and ending dates as parameters, it's even easier.  Just remove the date criteria in the formulas (in the case of @Lead_Cost, just remove the If..Then structure altogether, and just leave the addition).  Group on your dates by month, and put the Sum values in the Group Footer.  You can even suppress the details sections to make it all look like one big pretty table.