The amount of time that passes between an arrest and the filing of charges on the one hand, and trial or entry of a guilty or "no contest" plea on the other, varies widely from case to case. A misdemeanor drunk driving case, for example, might resolve within a month of the date of arrest pursuant to a standard plea offer. (Prosecutors often have a policy of offering a routine deal to certain kinds of offenders, like DUI arrestees without any prior convictions.) Felony trials can linger without resolution for over a year—and that's without accounting for any delay between arrest and the filing of charges.
However, once criminal proceedings have begun (with the filing of charges), defendants can generally force them to move relatively quickly. For example, in California, a defendant charged with a felony must be brought to trial within 60 days of being arraigned on an information or indictment unless there is "good cause" for delay—otherwise, the judge must dismiss the charges. (Cal. Penal Code § 1382.)
The time within which a defendant must be brought to trial can vary from state to state, and also depending on whether the accused is in jail. In California, in-custody defendants charged with either a misdemeanor or an infraction have the right to go to trial within 30 days of arraignment or entry of a not-guilty plea; 45 days is the time limit for those who are out on bail or their own recognizance. (Id.)
In-custody defendants often don't want to "waive" time, while out-of-custody defendants often do. There is no hard-and-fast practice, however, and defense attorneys usually have a strategy for recommending that the client either waive time or not.
If you face criminal charges, consult an experienced, preferably local, attorney regarding the time it might take to resolve your case and any other concerns you have. Only such a lawyer can protect your rights effectively and advise you as to your best course of action.