So supervision is something done above and beyond just having a boss at work. I'm a certified licensure supervisor in my state for LCSW, so I can tell you how we do things but YMMV depending on where you are.
First off, the requirements for the LCSW here are that you must have graduated from a CSWE-accredited school with a MSW. There was a period in the early '90s when the statutes were newly implemented that some non-MSWs got grandfathered in, so every once in a while you find a MEd LCSW or the like but that's increasingly rare. Secondly, you must have a "passing" score on the ASWB exam (usually the clinical exam, not intermediate or advanced). "Passing" varies by state- my state's is 70, but our neighboring state is 75. Then you have your supervised hours requirement...
Typically it has only been a LCSW (or equivalent) who is "qualified" to supervise a MSW for licensure. This is not to be confused with workplace supervisor; I've been supervised in a work setting by LPCs, MSWs without a license, and PhDs. But LICENSURE supervisor will most likely need to be a LCSW. A qualified licensure supervisor may or may not be available through your employer; agencies are not required to provide this, however most recognize that new grads consider it an added benefit. My supervision was provided at my job by someone who was NOT my direct work supervisor. What a blessing, as my direct work supervisor was bat**** crazy and got fired 9 months into my employment. After I was licensed, my company instituted a policy that if you signed up to be supervised in-house (either LPC or LCSW), you had to commit to working there a year post-licensure, or pay back $1000 if you left early (pro-rated monthly for each month you stayed). Some places may contract with someone to come in.. some places may tell you you're on your own. There are certainly private practitioners (myself included) who will offer supervision; your state committee for SWs may keep a list of these people. Some will charge the full hourly fee they charge to a client, some will charge a lower rate or do sliding scale, and some may offer supervision pro bono. If you are using a supervisor outside your agency, it is imperative that your agency be aware of this and that they are in agreement. After all, you cannot effectively do supervision without disclosing some confidential patient information. Written consents will likely need to be obtained. (I've seen it before where the agency officially makes the supervisor a "business associate", thereby skirting the "every client must sign a consent for the MSW to share info with the supervisor" thing.) Effectively, you wind up with your work supervisor AND your licensure supervisor, often not the same person.
On finding a supervisor, the supervisee then has to register their supervision, so the state can make sure it's an acceptable supervisor. Supervision consists of regular meetings to discuss cases, go over ethical issues, do education, etc etc etc. It needs to average to 1 hr/week, but can be done as 2 hrs e/o week or at max, 4 hrs 1x/mo. Some of this can be done in group supervision (ie 1 supervisor, multiple supervisees) but not all of it. Length of supervision is minimum 24 months AND 3,000 hours, no longer than 48 months. "Two years" is a good guideline if you're working full-time the entire time. Extend it if you're part-time or if you take a break in there. Once you're done, AND you meet all of the other requirements, you apply for your license. I have to fill out an "Attestation Form", verifying that we have done supervision and that I'm willing to stake my license on this person.
State statutes will direct you to how this is done. My state's Department of Professional Regulation website has all the info online, so check for your state.
As a side note, I really don't recommend that your work supervisor be your licensure supervisor.. as I said, my work supervisor got fired, which would have made a HUGE impact on my supervision (would have lost all those hours b/c no attestation form). Also, though, if you have serious concerns about how your supervisor or agency is doing something, it's nice to be able to talk with your licensure supervisor without fear of having professional consequences from raising your concerns. And finally, by going outside your agency, you don't have to worry about changing supervisors if you switch jobs in the middle- you can usually just stay with yours (in my state you just fill out a "Change of Setting" form).