How much does it cost to position for guardianship and how long could it take?

Varies according to your situation as well. For instance, if you want guardianship over an elder, and there is other members in the family who do not want you to assume this duty, and fight the guardianship in court this can go to 10s of 1,000s in costs. Also, if the elder doesn't believe he or she requires guardianship he or she will be assigned an attorney by the courts and can fight your request. This will make the costs rise as well. If you win guardianship some of this cost can be recovered from the elders estates in some instances.
If you have an incompetent elder and this person requires placement and care often a social worker in hospital or in rehab can help you to get emergency temporary guardianship.
You need also to be aware of all the is entailed in having guardianship and need to be ready, willing and able to do meticulous record keeping as you are taking on fiduciary responsibilities that you are legally beholden to do; failing in this task could result in criminal legal actions.
You would hopefully get more complete answers on Forum by giving more information. But in truth, with legal issues like this an hour of Elder Law Attorney's time is well worth it. Have your situation details and questions all ready and make an appointment.

This process will vary by state and probably even by county. I would consult an elder law attorney in your state for more accurate answers. On this forum I've read that it can cost up to $10K, but some people have done DIY and it's not so expensive but more time-consuming, probably if there's no family squabbling over a person or the person's impairment isn't in question. Timing may depend on whether it's an "emergency" or if the courts are clogged with cases.