You will need to have a background check, fingerprints, and a safety inspection as minimum, and will need to get training, but I know some states will place before the training is completed as long as it is done within a certain amount of time.
Different states have different requirements. This can take several weeks to several months.
If the children are located in a different state you will need an interstate compact agreement which can also slow things down also.
Like the others suggested, contact the case worker for the children and he/she can direct you and help you get started.
There are specific resources offered for Kinship fostering because of the special challenges it can create.
Your state may have a foster website that could offer good information on training dates, safety regulations, people to contact, etc.
I hope things work out for you and your nieces and nephews.