My dynasty league is 12 teams, 20 man working roster, 2 rookie taxi squad, 2 man IR. Going into year 4. No contract system or salary cap, i.e. pure dynasty.
We have our championship game in week 16, then allow one week of offseason free agency prior to the week 17 games. After that, free agents are off limits for the veteran draft in mid-late August.
Owners can enter the offseason (after week 17) with up to 24 players if they have their working roster, taxi squad and IR all filled. Actually the IR rules are relaxed for week 17, so there's no reason for anyone not to enter the offseason with 24 players. Owners can then exceed that number during the offseason to accommodate trades (but not through adding free agents). Our offseason trading begins after the Super Bowl, sometime in mid-February. Owners are allowed to trade draft picks up to one year in advance (e.g. 2007 draft picks during this offseason).
We have 2 drafts, one for rookies starting on August 15 and the veteran draft following a few days after the conclusion of the 3 round rookie draft. The vet draft is how ever many rounds are needed for each team to reach 22 players (assumed 20 for working roster and 2 rookies for taxi squad). All drafts are slow draft method. We have a cut down day several days before the rookie draft starts, and owners must get below 22 players at that time in order to make their rookie selections. All picks in the rookie draft are optional, but there is no reason not to make all your rookie selections. Once the rookie draft is complete, owners have a 24 hour period to cut additional players if they wish to have more vet draft picks. Our rookie order is set inversely from league finish the previous season, and order is same for each round (except that we have a trash playoff system for non-playoff teams for the first overall pick only; otherwise, all picks are set worst to first record). Vet order is set based on how many players are needed for each team to fill its roster (team with fewest players after rookie draft picks first), with ties broken by previous year's league finish. Free agency opens a few days after the vet draft is complete, and owners can start to utilize their IR at that time if they have players eligible for it.
Truthfully, you can make a case for not having a vet draft if you don't have a contract system or salary cap. The talent level is only waiver wire material with pure dynasty, so you can just choose to go straight to free agency if you want. It's a bit more orderly though to have a vet draft so you don't have 10 teams scrambling all at once to fill out their roster. Guess you can use a waiver order in that case, but then might as well just have a vet draft because it will end up working out the same.
As for why to have the rookie draft as late as possible rather than say in May; in a league where the only real way to tool your roster is through the rookie draft, best to make sure the weaker teams that "earned" the highest rookie picks have as much opportunity to assess their place on the depth chart and what their opportunity is going to be with their new team. Some will say the earlier the draft is, the more opportunity for the sharks to separate themselves from the guppies, but that also opens the door for longer rebuilding projects, more rundown franchises, and more chance for weak owners to abandon ship and leave a league behind scrambling for new ownership for unattractive franchises. And that's not a good situation for any dynasty league.