My favorite way to get between the two used to be on a United Express Embraer-120 operated by SkyWest, which gave you a grand aerial tour of the LA basin and, at the time, 500 frequent flyer miles for 34 flight miles. Sadly, those flights were discontinued some years ago.
Shared Van
As with DAL-DFW, MIA-FLL, or HOU-IAH then, the most direct and economical LAX-SA transfer would be a shared van service (if traveling alone). At present, SuperShuttle and Prime Time Shuttle are the concessionaires. SuperShuttle's website quotes $36 for the first passenger and $9 for each additional passenger.
There are two main problems with shared vans, at any major airport:
- You could have up to 8 fellow passengers going to up to 8 different destinations. If you are the last passenger to be dropped off, it could be a couple of hours before you reach your destination.
- LAX being a huge airport, there will probably be vans headed to John Wayne or its environs throughout the day. But, on the flip side to #1, this can mean waiting for the van to fill, whether it's others who have made a reservation or walk-ons. So the time you save on stops is somewhat negated by the time you sit on the curb for other SNA-bound passengers to materialize.
Still, at $36 (and $1–2 for the driver for each bag s/he handles) and a couple of hours, this is probably the best trade-off you will find.
If you want an exclusive van, the charge is $95 total for up to 9 people, though if it's privacy and directness you need rather than capacity, you might as well book a taxi or ride service.
Taxis and Ride Services
According to TaxiFareFinder.com, a one-way metered taxi ride from LAX to SNA is about $135, which includes the $4 airport surcharge, $113 fare, and $18 tip. Unfortunately, almost the entire length of the trip will be along the notorious 405 freeway, which is unpredictable. Thus, your fare could end up $10-15 higher, and range from 45 minutes in ideal traffic conditions to double that in bad traffic.
Uber and Lyft charges vary according to demand and driver availability. Right now (Monday around 9am Pacific Time), the low-end UberX is quoted at $46-61, and the super high-end UberLUX $233-303.
FlyAway to Downtown + Trains
The FlyAway bus, a flat $8, is the easiest way to get to downtown Los Angeles from LAX via public transportation. Now, DTLA is in the wrong direction from where you want to go (northeast as opposed to southeast of LAX), and a good 45 minutes away, but if you have time to kill and want to save a little money, this option is not entirely crazy.
I outline several downtown to JWA train/bus and train/taxi combinations in Traveling from Downtown, Los Angeles to John Wayne Airport . If your friend lives near SNA, he or she almost certainly has access to a car, and if they were willing to pick you up from the airport, might be willing to pick you up from a MetroLink or Amtrak station nearby.
Disneyland Shuttles
JoErNanO has already pointed out the possibility of going via Disneyland using Southern California Gray Line. Competitors include Mickey's Space Ship Shuttle (put on sunglasses before opening that website) and Disneyland Express. As the Disneyland Resort is a common destination from both airports, you can piece together a trip
The downside is that Disneyland is not along the most direct route from LAX to SNA, and thus you will spend more time, and risk more traffic jams, traveling to and from Anaheim. Additionally, as JoErNanO has also pointed out, these services are not primarily aimed at inter-airport transfers, so the schedules will not be coordinated, and you may end up waiting a good while at Disneyland's bus depot, which is notably less magical than the park.