The three main actions are:
1) Roll dice
2) Move token
3) Pay the "piper" (rent, purchase price, fine, or go to jail) as the case may be. In the case of some chance or community chest cards, you may receive money.
The two "stickier" issues are trades and property improvements.
Most interpretations of the rules say that you can trade properties or other consideration (get out of jail free cards) at any time. That's because it takes two players to make a trade. The one caveat is that if you have landed on something and owe rent or a fine, you cannot trade property until it is clear that you can pay the rent/fine from other sources.
The main question mark is regard to improvements. Here, the official rules are not clear. In many games, there are "house rules" that say a player may buy and sell improvements (including mortgage and unmortgage) only during his/her own turn. Another set of "house rules" say that a player may buy/sell/mortgage property only at the BEGINNING of a turn (before the dice have been rolled). Basically, these rules are meant to prevent players from buying houses and jacking up the rent AFTER someone has landed on a property. In "real life" you couldn't just move a house onto property where people are "staying;" the house would have to have been built beforehand.