Here goes:
Anions either sulfate, phosphate, chloride, carbonate.
1. Fresh sasmple - add H+ ions eg. HNO3. If bubbles occur, then carbonate ion is present.
2. Now to the solution, add Ba2+ ions eg. Ba(NO3)2. If a precipitate forms then sulfate is present. You may note from solubility tables that Barious phosphate is also insoluble. However, this formation of the precipitate only occurs in basic solutions.
3. Now to the solution, add Ag+ ions. If precipitate forms and turns dark purple in sunlight, then Cl- ions are present.
4. Finally, to the solution, add ammonia which increases the pH of the solution. Because you already added Ba2+ ions into the soln in step 2, if phosphate ions are present in the mixture, then Barium Phosphate precipitate will occur.
Now cations - either Cu2+, Fe2+, Ca2+, Ba2+, Pb2+
1. Firstly, add HCl. All chlorides solluble except for Pb2+. Thus if precipitate occurs, then you lead is present. If present, filter and continue using filtrate in step 2. If not, take a fresh sample of the mixture.
2. Add sulfate ions eg. H2SO4. Sulfate will form precipitate with calcium or barium. If a precipitate occurs, to determine which it is, take a sample and add F- ions. If a precipitate forms, then Ca2+ is the cation. If a precipitate doesnt form, then Ba2+ is the cation.
3. So now we got Fe2+, Cu2+ left .. Add OH- ions. Both ions could form precipitate with hydroxide. however, we can distinguish which is which by colour. Cu(OH)2 is pale blue and Fe(OH)2 is plae green.
Refer to Conquering Chemistry for flowcharts on this procedure. If you do not have time to memorise, make sure you know your solubility tables!
Cheers! and best of luck. =D