Say you have 3 acidic protons (2 -COOH's and one -NH3) in 1 molecule with the following data:
pK1=1
pK2=3
pK3=9
At a pH of:
14: [OH-] is so high and [H+] is so low that we can rest assured that all sites are deprotonated and the predominant species is A2-.
10: Much the same as 14 but also some HA-. Keep in mind that the sites with pKa =1 and 3 are still completely deprotonated because the pH is still way too high for that.
9: pH=pK3 so [A2-]=[HA-]. As above, the other two sites are still completely deprotonated. This means that at this pH there's an overall -1 charge on the average molecule.
Since we need the average charge to be zero for isoelectric pt, we still have a way to go. Let's skip for a moment to pH=4.
4: At this [H+]we can rest assured that site 3 is "completely" protonated. There are essentially no molecules having a deprotonated site 3 at this pH. As for the other two sites: for site 1, pK1=1, we can still assume that it is completely deprotonated. Even site 2 can be assume to be predominantly in the deprotonated form because pH is one unit higher than pK2, which means (from Henderson-Hasselbach) that the base form is 10 times more predominant that the acidic form. So at this point we have a +charge on site 3 and two - charges on sites 1 and 2, giving an overall charge of -1. NOT MUCH CHANGED between pH 8 and pH 4. The -NH3 remains positively charged below pH 8 no matter what.
We need to get a -1 charge to balance the +1 charge on site 3. What this means is that we need an average of 0 and -2. If pH=0, all sites are protonated, leaving us with an overall charge of +1. So we need to find the average between pH 0 and 4: (0+4)/2=2. This means that at pH=2, the average charge between sites 1 and 2 is -1. Since -1 balances the +1 the isoelectric point is 2.
Remember, that after we move from pH 8 on downwards we do not need to worry about the status of the -NH3 group. It remains protonated (and more so!) all along.
Hope that helps.