DynastyLeagueFootball has a great summary:

A dynasty fantasy football league is a league where you retain most or all of your players from year to year. This creates an environment which is very different from that of a redraft league. By enabling team owners to keep players and build a team over time, there is a much stronger sense of team ownership. Success is achieved with a greater sense of satisfaction. Mistakes or successes in a dynasty league can affect the fortunes of a franchise for years to come, just like in the NFL. A dynasty league also facilitates trades, including trading of draft picks, and it encourages a deeper roster pool, so young ‘project’ players can be identified and groomed.

Dynasty is becoming a more popular format because it is the closest simulation to being a real general manager. Decisions around how to value youth, how to construct a roster, and which trades to make or take has lasting impact on your franchise.

Unlike redraft leagues, dynasty leagues are typically active year-round. Owners pay close attention to the, NFL Free Agency moves (e.g. Odell to the Browns, Howard to the Eagles), NFL combine, NFL draft, and actively chat with each other in friendly banter and trade talks during the off-season.

Getting Started - Recommended Settings for Dynasty Leagues

We recommend the following settings for Dynasty Leagues if this is your first season doing dynasty:

12 teams

18 roster slots

2 IR slots

3 Taxi slot (Further explanation on Taxi slots here)

This will ensure each team has the opportunity to develop young talent while making sure that the waivers still have something serviceable to pick up each week.

For scoring settings, you can just use what you are already comfortable with in your redraft leagues, whether it be PPR, Standard, or half-PPR.

Selecting a Host Site:

This is one of the most important decision that you will make. There are so many options which will accommodate your dynasty league. You'll want one that's affordable, meets your league requirements, always improving, and great customer support.

Here's why you should pick Sleeper.

Sleeper is open 365 days a year. Unlike other apps, you can trade picks (No more google spreadsheets, excel, etc), slow draft (overnight), do a vets and rookie draft separately, and allow offseason moves so that can make moves during the free agency frenzy. Always open. Love it.

More importantly, Sleeper's best-in-class chat features, modern user interface, and native mobile apps make us a natural choice for dynasty leagues seeking a permanent place to call home. We know you love winning, but let's be honest. You're playing with your closest friends, so it's usually about camaraderie AND winning.

Existing dynasty league hosting sites are very outdated in terms of design, lack mobile apps, and even charge money. Our platform offers the first modern experience for the dynasty player — and is completely free. Plus, no ads. No overlays, banners, pre-roll, pushdowns, pushups (yes i made up a word), etc.

You can get started here: https://sleeper.app/fantasy-football

Finding a League: Join vs. Create

If this sounds interesting to you, then make the plunge into year around fantasy and find / create a dynasty league.

Join a league

You can usually find free dynasty leagues either in Sleeper's Fantasy Football Chat Channel or r/findaleague. I would recommend against taking over an orphan team (the owner left), because it usually takes 3+ years to turn a team around. It's so much more fun joining a league from Day 1. If you don't know anyone starting a league and you've tried both of those sites, hit us up on Twitter and we'll help!

Brand new dynasty league

To start a new dynasty league, simply create a new league, and choose Dynasty as the type.

Convert an existing Sleeper league to dynasty mode

If you played in Sleeper leagues last year and want to renew it as a Dynasty League, you can simply “renew” the league and choose Dynasty as the option.

Move from another platform to Sleeper

If you were on MyFantasyLeague, FleaFlicker, ESPN, CBS, NFL, or Yahoo! previously and want to continue your dynasty league on Sleeper, the easiest way is to fill out a draftboard with the players in the slots, then create a league out of that draftboard by “completing” the draft as the commissioner.

If you want to do your Rookie draft on Sleeper, simply select “Add Supplemental Draft”.

Detailed steps can be found here:

How to move my dynasty league over to Sleeper from another platform

Draft Pick Trading

All Dynasty Leagues have draft pick trading enabled by default. You can now trade picks along with your players, or just picks themselves!

"Allow Offseason Moves" setting

If you turn off "Allow Offseason Moves", league mates will be able to trade, but will not be able to make any FA/waiver moves. If your league has a trade deadline, league mates will be able to trade again once fantasy playoffs end even if this setting is turned off.

Empire Leagues

One of the biggest problems with dynasty is that people end up leaving after 1 or 2 bad years. You can combat some of this behavior by making your dynasty league an empire league. Empire leagues will not pay out 100% of the dues every year. Instead, a portion of the annual dues will go to an ongoing side pot. When a league mate meets certain criteria (e.g. winning the league two times in a row, or winning 3 times), then the side pot will be awarded and you'll start all over again with a brand new draft the following year. At Sleeper, we love empire leagues. Do it.

Finally, recommended places to research for your dynasty draft

Here are some great places to do your dynasty research. Note that in dynasty, younger players are favored a bit higher, as well as WRs as they tend to have longer careers.

One final note: DO NOT RUSH IT. Dynasty is not for everyone. If you want to take it seriously, take your time with it and fill a league with the right league members (these could be friends IRL or people all over the world). If you end up with some bad apples, again, take your time with finding the right members to re-fill the league.