What do I have to do to get joint parenthood or joint custody of my son?

If you do not have orders in place yet, then you need to file a custody suit.  You do not mention if you and mom are still married, but if you are, you can combine the custody suit with the divorce.  Courts will decide custody based on what is in the "best interest of the child."  When parents are reasonable and can get along, the courts actually prefer joint custody.  Just because mom doesn't like the idea of driving to meet you, doesn't mean the courts cannot require that of her.  Stay focused on "reasonable", and you'll have more luck with getting joint custody with favorable terms.  For example, present two options-- meet half-way each time or one parent drops the child off one way, while the other drops the child off to the other after visitation--- that way neither parent is burdened by the expense of the visitation.  A fifty-fifty split of the child is probably not going to be possible because you live so far away and the courts will not want the child bouncing at one school for a couple of days, and then jumping to another school district for the remaining days of the week (when the child reaches school age).  However, you can still ask to have almost all of the same rights as mom:  to consent to medical treatment, right to be involved in education of child, etc...  Even with joint custody, only one parent will have the right to determine the main residence of the child.   

If you already have some type of orders in place, then you simply need to request a modification to accomplish the same things discussed above.  Whether you seek joint or sole custody, make sure that you are able to demonstrate to the court that you intend to be a good parent for your son.... like he has a bed of his own to sleep in, child care support, family members close by to give you support, parks nearby for th child to play at... this is not an exclusive list, but it demonstrates to the court that you've put thought into being a good parent for your child and you should have an opportunity to have solid time with your child even though he is only 6 months old.

If you want joint legal and physical custody of your six (6) month old son, I suggest that you consult with a family law attorney to see what legal resources are available to you in your endeavor. Most likely you will have to file a petition in the county court house where your son resides seeking joint custody of him with the mother.

Based upon the pleadings and declarations submitted, the court will make a decision as to your request.