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Depends on the polity. For example, here in California in four weeks' time I will help select a variety of executive, legislative and judicial officers, from my representatives in the California legislature to Congress, the US President and Vice-President, councilmen for my city council, commissioners for my local community college district and water district, and whether to retain or fire several Superior Court judges. Then there will be the opportunity to pass or reject a number of laws placed directly before the people as ballot initiatives. I believe there are about eight, that deal with everything from raising state taxes to requiring the labeling of food products a certain way and prohibiting union dues from being used as political donations. (It's a fat ballot, and takes forever to figure out.)
Then there's the fact that not long ago I was called for jury duty in Superior Court. As a juror, one has the opportunity to decide how, and even whether, a law is to be enforced. A somewhat lesser-known fact is that a jury is perfectly within its rights to decide that a defendant is not guilty because the law under which he is charged is unfair or unreasonable. This is sometimes called "jury nullification," and is a rarely used power.
A few years ago, we had a recall election here in California, where enough people petitioned the state to recall from office Governor Gray Davis. An election was scheduled when the number of signatures reached a certain number, and he was indeed recalled.
Similar things can happen for more local issues: a group of parents in a LA school district, angered that the local public school system was unresponsive to their concerns, used an unusual feature of the law that allows a sufficient number of parents to demand that a school district be taken over by the state, removing from power the local school board.
Opportunities to participate in making of law, both directly and indirectly, abound. There are still villages in New Hampshire were essentially the local village ordinances are decided by all the adult residents getting together on folding chairs in the school auditorium and hashing it out, taking votes where necessary.
(1) Election of legislators, executive officers (governors, President), and sometimes judicial officers (where they stand for election, or confirmation) at regular elections.
(2) Confirming bills put before it by the legislature in referenda, and passing laws directly by initiative.
(3) Recalling executive officers by special recall election. (I don't know if legislators can be recalled. Senators, maybe.)
(4) In more local affairs, sometimes direct democracy.
Of course, there are a bazillion indirect methods for pressuring lawmakers, e.g. writing them, writing them checks, talking at townhalls or open council meetings, publishing scurrilous attacks on them in the press, making mocking Youtube videos about them, and on and on.