I will be arriving at Islip airport on a tuesday morning and need to get into NYC. I want to take the Ronkonkoma train into Penn Station.
Can someone give me detailed step by step instructions for a plan to follow. Please help with what I should expect to pay for each part. I do not want to take a taxi. Thank you.

There's a shuttle from outside of baggage claim to the Ronkonkoma train station for the LIRR into Penn Station. I have no idea of cost but it runs every half hour.

the schedule really depends...
rush hour, or mid-day. there are certainly more trains at rush hour, but after 11am or so, it will be less frequent. the website for schedule and fares is www.lirr.org.
it's probobly $12 or so for a one way ticket. (i only ever had the monthly passes, so not exactly sure...) you can by tickets from a machine with debit, credit card, or cash before the train. if you buy it on board the train, they charge you quite a bit.

The shuttle at the airport charges something like $2-5/person to take you to the train station.

Here's the link to the train schedule.
http://www.mta.info/lirr/html/ttn/ronkonko.htm
Prices fluctuate depending on which train you take. It may be possible (and less expensive) to buy the ticket online now.

PS the trains are only every half hour during rush hour (up to 9:15am). After that they're once an hour.

The airport shuttle runs every 30 minutes but outside or rush hour the trains run only once per hour. Depending on when you arrive you may want to spring for a cab to the train station to avoid a longer wait.

There are no cabs to the city. You can organize a car service - but the cost is about $125.

The train from Ronkonkoma to Penn Sta takes about 1:15 and costs $15 one way off peak (after 8:30am). The trains run once an hour except for a few extras at rush hour.

is this a direct train to Penn Station? I can make the 12:11 train hopefully.

It is direct in that you won't need to change trains. It makes multiple stops between Islip and Penn Station.