You first need to fine an employer willing to offer you a full time job. That employer must then obtain an approved LMIA. The LMIA requires the employer to advertise the job for at least a month before submitting the LMIA for processing. Processing typically takes 2-4 months. Once the LMIA is approved, you then have to apply for a work permit. So the 4-6 month time frame is about right - excluding the time it takes you to find an employer.
Generally speaking, it's extremely difficult to impossible to find employers willing to go through the LMIA process (because it is long, expensive and has no guarantee of approval). Also, it's quite possible the LMIA could be refused if the employer should have been able to find a Canadian for the job.
Note that the job you get must be skill level A, B or 0 in order for you to qualify to bring your family with you.