The following is provided by lemonelephant, the mom of a Sailor.

It will take about a month before your Recruit will be paid because it takes a while for everything to get entered in the system, but be assured, your Recruit will receive the pay from the day he/she was sworn in at MEPS on the way to the RTC. Pay days are the 1^st and the 15^th, but those who choose to have the pay directly deposited into a Navy Federal Credit Union account will see the deposit a day earlier. Here are some examples of when others have received that first deposit: arrived March 8 – deposit March 31 (this Recruit must have chosen NFCU), arrived December 2 – deposit January 1, arrived May 28 – deposit July 1, arrived May 20 – deposit June 15. It would appear that Recruits in TG 47 should receive that first deposit on or before the September 15 pay day. You can be pleasantly surprised if a deposit is made earlier than that.  Some in the group indicated that their SR was paid on August 31 or September 1.

They don't get paystubs. Their LES (Leave and Earning Statement) is online at mypay.com. The mypay account appears to be set up by the recruit at some point during the first week or so of BC.

It will take 3-4 pay days for the pay to settle at what will be the norm for your Recruit/Sailor. Pay days are the 1^st and the 15^th and they will be paid half of their monthly earnings on each pay day. Remember that state and federal taxes are taken out as well as the premium for life insurance (SGLI, which is about $27 a month). The first few deposits are not the same because the first deposit is prorated from when the Recruit first arrived and that deposit and/or the next one will have deductions for the NEX card the Recruit is issued for the things for the Seabag and things that are needed at BC and for uniforms. Note that they get a uniform allowance, so money is put in and then taken back out for the various uniform parts. The pay depends on their rate.

If something happens and a Recruit is sent home, he/she will be paid for that time.

BAH (Basic Allowance for Housing) does start from day one, but you won't see it in the accounts right away. In fact, some don’t see it until after the Sailor has left boot camp.

Medical coverage for Recruits begins as soon as they swear in at MEPS, as does life insurance. Dependents are also covered under medical from day one. The Recruit must enter them on page two and get them enrolled in DEERS (Defense Enrollment Eligibility Reporting System). This happens the first week in processing during boot camp.

The link, Navy Pay Charts, provides information to help figure out the pay and BAH.

This is the calculator for BAH, it is based on the zip code where the dependent resides.
http://www.defensetravel.dod.mil/perdiem/bah.html

Here is the Navy Pay and Compensation Calculator.

https://staynavytools.bol.navy.mil/PCC/?B3=Launch+Calculator (You may not be able to open this. I can some days and can’t on others.)
Enter the Sailor's pay grade, date of entry, tax filing status, dependents, DOB, ZIP code, etc. and out pops all the pay and compensation (BAH, BAS, uniform replacement, etc), both gross and take home. It shows the tax breaks (allowances aren't taxed!), the value of benefits not in the pay check (free health care!) and projected retirement benefits for career Sailors. Your Sailor MAY get up to $4000 a year from the Navy College Program if taking off duty classes (a grossly under used benefit).