First, a protein at its isoelectric point is neutral - meaning that the net charge is zero - meaning that the groups are COO- and NH3+
An amino acid will have 3 pka values (except for glycine which has 2). Lets call them pka 1, pka2, pka3. They of course have their own corresponding pH value or [H+]
Pka1 corresponds to the carboxyl group, Pka2 corresponds to the R group, Pka3 corresponds to the amino group. It is possible for the R group to be pka3 and amino group to be pka2, but, you would be told this is the question through words or a graph. However, lets assume what I said earlier corresponds to the protein we are discussing. An increasing pH will encounter pka1, pka2, and pka3 respectively.
A pH below pka1 means that the carboxly group is protonated. This is because many H+ are present in the relatively acidic solution. Because we are also below the other pka values, this means that all of the other groups are also protonated. By the way I am speaking relatively meaning that the concept is basically the same for all amino acids. It is just that the pka(s) differ in their value.
Between pka1 and pka2: the carboxyl group is deprotonated while the R group and amino groups are protonated.
Between pka2 and pka3: the carboxyl group again is deprotonated, the R group is deprotonated and the amino group is protonated.
Above pka 3: Everything is deprotonated including the amino group.
If the carboxyl group is deprotonated it is -1 charge. If the amino group is protonated, it has a +1 charge. The R group of course depends on the group or if it even has an amino group or carboxyl group as aliphatic R groups have no effect of the pka graph.
Determining charges of amino acids depends of the pH the AA is in. For example, "negatively charged and positively charged" AA are called that because they are at physiological pH (7.4pH). So, to assign charges you must look at all the pkas with respect to the pH of the solution and evaluate which ones will be positive, negative or neutral and finally add up the charges
I would like to bring up a question: An AA, with a R group that is amino or carboxyl, at it's pI has a COO- groups and NH3+ group; is the R at it's pI? I believe it is. Please correct me if I am incorrect on something above. Thanks