What are the oxidation numbers for the elements in these compounds?

Rule of thumb: H is nearly always 1+ and O is most of the time 2- (but there are exceptions! see #2)

1) H is 1+ but you have 2 of them, so 2+ total.
   O is always 2-.

2) H is 1+ but you have 2 of them, so that's 2+ total. O, however, cannot be 2- this time since this molecule is neutral. O must have a 1- charge; you have 2 of them, so 2- total.

3) O is 2-, but you have 3 of them, so 6-. Cl must be 5+ in order to make the -1 charge.

4) PO4 (phosphate) has a 3- charge, with 4 of them that means it's 12- total. That means Lead (Pb) must be 4+ to cancel out the 12- (since there are 3 leads).

inside phosphate itself, oxygen is 2- x 4 x 4 = 16-. P is 4+ x 4 = +16.

Hydrogen always has an oxidation number of +1, and oxygen is either -1 or -2.  The oxidation numbers of the individual elements in the compounds should add together to equal the overall charge on the compound.  
In #1, the overall charge is zero, so the oxidation number of hydrogen +1 (x2 because there are 2 hydrogen atoms) - 2 (oxygen) = 0.  
In #2, we know that hydrogen is +1 (x2), so oxygen must be -1(x2) to equal zero.  
In #3, oxygen's number is -2, because it is only -1 in peroxides.  Thus, in order to equal an overall charge of -1, chlorine's charge must be +5
 [5 - 6 = -1]
For #4, we need to look first at the phosphate group (PO4-3).  We know that oxygen's number is -2 (x4), so phosphorus must have a number of +5 to equal an overall charge of -3.  Now, since we have four phosphate groups making a total of -12, the oxidation number of the 3 Pb atoms must equal +12 for an overall charge of zero.  So, 12 divided by 3 atoms equals an oxidation number of +4 for lead.