NOTE: This answer is valid only for the next few months. Sometime in (or after) April 2019 the “IST” airport is moving to a new location, which will change many of the options…
How simple it is depends on how much you’re willing to pay.
The two airports are roughly 60-70km apart (depending on the route). The simplest option between them is to catch a taxi. The time this takes (and the cost) will depend on the traffic and thus the time of day, but could be anywhere between 40 minutes and 2+ hours and cost somewhere around 200 TL (possibly more with very bad traffic).
There there no direct public transport between the two, however Havabus has a services from IST airport to Taksim, and from Taksim to SAW airport. This will cost around 32TL, but realistically will likely take well more than 2 hours, and even longer if there is traffic.
Havabus also have a service from Kadıköy to SAW which may be slightly faster than taking the bus the entire way, however this would require catching the Metro and then a Tram to get to Kadıköy, and is not something I would recommend if you’re not familiar with the area.
The real catch with this transfer is the traffic. IST is on the European side of Istanbul, whilst SAW is on the Asian side, which means you have to cross the Bosphorus – which means going over one of 2 bridges or through a tunnel – all of which suffer extensive congestion much of the day. Allow more time that you expect it will take, especially if you’re going anywhere near peak-hour – which can realistically account for most of the day and well into the night…