My first bit of advice.
This would apply to teams that managers have determined have fallen out of contention, and have several productive assets that hold some trade value.
We will assume here that your league enforces anti-tanking rules, things like draft lotteries, or perhaps by having minimum games played limits - or maybe a minimum salary-cap threshold that must be met. You don't need to cheat, but feel free to push the rules when you can. One thing to try would be to lobby rule changes in the offseason that would benefit a rebuilding team. Maybe lobby to have additional bench spots, or change scoring categories that might create more trading in your league - anything that might make your rebuild shorter.
Your own draft picks are now your most valuable asset, and absolutely must be hoarded. These picks will be a big part of the rebuild phase, and the lower you sink in the standings, the more valuable these picks will become. Moving your productive players for additional picks and young players will serve two purposes, it will add more future pieces to your rebuilding plans, but also moves your picks further up the draft ladder.
The main piece of advice I want to share here, is that teams can teardown too much. You really only need to teardown enough to sink into the draft lottery, and can often keep an asset or two that will jumpstart your rebuild. Tearing down to bare-bones only serves to lengthen your rebuild.
There are sometimes ways to increase the value of your draft picks without a major teardown. Example, in some H2H league set-ups owning the league-worst goalies will rack up the losses for your squad and potentially put you in the draft lottery.
Feel free to comment, or add your own experiences rebuilding a fantasy team.