This post could probably be entitled how to get a job in (fill in the blank competitive market) because getting a job anywhere requires similar skills
Step 1 - prepare
-make sure you have an updated CV, make it look professional, turn it into a PDF so that it can be emailed easily.
-write your cover letter - this should state you desire to move to your desired location as well as highlight your strengths as an applicant. This will sometimes be all employers look at so make sure that an employer will see it and say "wow this is an interesting candidate and someone I would like to learn more about"
Step 2 - recon
-Know you targets a.k.a google effectively
a) hospitals - make a list of all their numbers
b) anesthesia groups - Some of them have websites and will show which hospitals they service. This makes life easier because they will often have a secretary where you can contact directly to submit your CV
c) understand what to reasonably expect - want to make 400k working 40hrs/week? not gonna happen. SoCal is expensive and you won't be paid as much as elsewhere. Understand that and accept it
Step 3 - figure out who matters
-When you don't know which anesthesia group runs which hospital, call the OR desk and ask to speak with an anesthesiologist and figure out which group runs the OR
Step 4 - work the phones
-Call the various hospitals and anesthesia groups, make sure you get the names of people you talk to and what they said. If you leave a message,make sure you know who you left a message with and what day you left it.
-Be persistent - don't call everyday but if you left a message and haven't heard anything call back next week. If you spoke to someone who said they'd call you back next week, call them back in 2 if they don't call back. If someone says they're not hiring right now call back next month. Make sure they know who you are but don't be annoying
Step 5 - expand your horizon
-every physician in SoCal wants to live by the coast in LA or San Diego which means those hospitals always have a ton of applicants. The good news is that this is a highly densely populated area and there are many jobs to be had. The bad news is that there are many applicants. This means that you might have to get your first job in the inland empire, palm dessert, el centro, or other less desirable location. It's called paying your dues and unless you know someone or have a highly desired fellowship you'll likely have to start there. What is a highly desired fellowship? That depends on the group, some like peds, others hearts, others pain.
-Don't be afraid to take a "bad job" just to get to the area. As long as the check cashes it's all good. Sure you may be working longer hours for lower pay but at least your in the area once you've got a foothold you can get your name out and get into the more desireable groups/areas.
-Surgicenters - don't be afraid of working at surgicenters if you need to. It might not be full time work and might not be the types of cases that you want to do but it will pay the bills.
Additional considerations
-Your SO - are you going to be the primary breadwinner? If so your SO needs to understand that your job comes first and they might have to sacrifice something in their life to make it work. If you are not the primary breadwinner you've got other issues to consider. You might be even more geographically confined than you first realize
-Kids - You might get a job in a great place where you want to buy a house and raise your kids but then again you might end up in a less desirable area. How's the public school situation? Will you have to afford private school? Do you want to settle down or are you going to continue to look for a better area forcing your kids to move and change schools?
-Housing - Buying a house ain't cheap, selling a house is expensive, and moving sucks. If you move at the wrong time you could end up oweing a lot of money if you bought a house. Are you OK renting an apartment for a few years until you are sure you have the job you want? How does your SO feel about this
-Luxuries - as you've heard other people state numerous times on this forum, the worst thing you can do when you first start out is buy a large house and expensive car. This goes double fore SoCal b/c you may not have the job you want and you need money to move or live on in between jobs. You don't need to live like a pauper but don't plan on going to Europe right away or throwing parties like diddy. If you don't have kids it becomes much easier to control expenses but if you have them you need to have an even larger cushion for unexpected expenses
SoCal is a great place to live but it certainly requires a little bit more work than getting a job in other locations. Only you and your SO can figure out if it's the right move for you but please consider everything that I've written and pay special attention to the additional considerations section. Good luck