Most people have associated anarchy with chaos, lawlessness, and a general Mad Max-style existence. This is not what it really means, just as "gay" originally had the meaning of "happy".
Breaking the word down, "an-archy" means "no rulers" just as "mon-archy" means "one ruler". (And "demo-cracy" means crazily ruled by demons. I kid. :) )
What this means in simple terms is that a society based on anarchy has rules; they tend to follow "common law" which has built up over centuries as a reasonable method to resolve disputes. Nobody in that society has the "special exception" to be able to break the rules.
That's pretty much it! In such a system, police would not be able to deprive someone of their property simply for traveling, regardless of the speed they were traveling at, as long as they hadn't injured anybody. Nobody would be hassled for making mutually beneficial contracts among themselves; if the contract was broken by one side, then the other side could seek redress. So many current "crimes" would be eliminated! And by certain professions no longer being criminal, the courts would also be able to resolve disputes in those endeavors, rather than resorting to gang-style drive-by shootings, or other vigilante means.
I mean, look at the below chart! Almost half of all incarcerations in the US are done for drug offenses. Half our expenses in kidnapping and extorting The People would go away!
Image from https://www.bop.gov/about/statistics/statistics_inmate_offenses.jsp, sort of; they have some stupid code to prevent us from copying the image, it just showed up as a white box here, and even when I right-clicked and downloaded it! Alt+PrintScreen and mspaint to the rescue. But seriously, "our taxes" pay for this government web site, and they're trying to restrict our use of it??!? Anyway, back to the narrative...
Services would be paid for on a usage basis, and there would be competing services -- several different fire protection services, for instance, which wouldn't only respond after a disaster; they'd also help create conditions to avoid disaster. Like helping with building design; concrete block structures tend to stay up better in adverse conditions, but are not so easy for "law enforcement" to break into, so most city and state codes specify "you gotta build your shit outta wood so we can huff and puff and get in when we want." Loosely translated, of course.
Thanks for taking the time to read this far. I used to be libertarian, small-"L" that is -- I tried doing politics a few times but there are too many lies for this logic-based brain to wrap itself around. Graduating to anarchy took some time and exposure.
I very much enjoyed Larkin Rose's book, "The Most Dangerous Superstition" (which is the belief in authority -- and that isn't a spoiler, as he divulges this on the first or second page).
My next book purchase will be "Freedom" by Adam Kokesh. In fact, let me go purchase it now: done! And wow, the Kindle version is only 99 cents! Also, Adam is on Steemit; I encourage you to follow him if you are interested in liberty and freedom. His account is 
[Edit: just found that Larken Rose is here as well! 
Blessings to you and your family for your continued health and prosperity.
, thanks!)