Before you can get onto Bituach Leumi you have to have been in the country on a visa for 183 days (6 months). The 183 days don’t have to be done in 1 go.
You then need to fill out 2 forms 1 for thr whole family and 1 for each member of the family.If you have kids you should also fill out the kitvah yeladim forms although you don’t have to do this to join Bituach Leumi.
When you apply for it you need 2 take with you 2 copies of your contract, your passports (the picture page and your visa page).If you are in yesshiva aletter from it.
You also need your whole families daf knisot veyetziot which you can get from Bituach Leumi.
In the mir you can get the forms and a letter telling you exactly what you need to take with (I’m not sure if the list above is 100 percent right)
A few weeks after applying you should get a letter from them with your Bituach Leumi numbers you have to take them to the post office with your wife and choose which kupat choilim you want to be on.
You will also get a bill charging you lemafraya for the last 6 months for Bituach Leumi.
After going to the post office you need to go to your kupat choilim and let them know about the changes.
You can then claim your money you have spent the last 6 months on kupat choilim back. You have to send a letter to someone I don’t remember who but its also on the mir paper.
Any more questions feel to ask.