Some common ions, such as halide ions, copper ions, zinc ions, and ammonium ions can be easily tested.
Halide ions will react with silver nitrate #(AgNO_3)# to give coloured precipitates of silver halides. For example, chloride ions will react with #AgNO_3# to give out silver chloride #(AgCl)#, which is an insoluble white precipitate.
Copper ions are usually in their #+2# state, and are blue in coloured solutions. To test for them, simply add some sodium hydroxide and a blue precipitate of copper(II) hydroxide #(Cu(OH)_2)#will form.
Of course, there are many other tests, and these are the basic ones.