Be careful and read the question asked!
A conviction is not the same as a no contest for either a misdemeanor or a felony. Normally, a felony conviction will work against you. A misdemeanor, depending on the exact seriousness of the crime and how long ago you were convicted, might still keep you in consideration. A no contest, although not great, might still keep yoiu in consideration
Bottom line, answer the question TRUTHFULLY, but do not volunteer detailed answers - unless they ask for it on the application. Be brief. If you have to check yes, then whatever you write, mention that it was "something you were not proud of, you learnt your lesson and have moved on". Turn a negative into a positive but DO NOT LIE on the app. That would definitely be the kiss of death when you get hired and they do your background check and bingo they find the rap sheet which you just happened to omit from the app. If you get the interview, handle that in the same way. Most employers will value your honesty and integrity.
An example to a "have you ever been convicted, pled guilty or no contest to either a misdemeanor or a felony?" question might be:
In 1995, pled "no contest" to a misdemeanor charge unrelated to alcohol (DUI), drugs or Part 108 Airport Security. No findings by court, Mar 1996. If the question asks about misdemeanor convictions and you have none, then the answer is simply NO.
The most pointed app question I have seen, is " have you ever appeared in court for criminal proceedings?" Of course, this includes everything and you have no leeway in answering that one. But a straight conviction on a misdemeanor or felony is easy enough to answer.
Also, I would strongly suggest that you go to the court and check your own records to see what is still on file. You need to check both the police record and the minutes of the court hearings you attended. One is a police record on your arrest/booking/charge, the other is yr legal proceedings and eventual case disposition. The police check is normally available for a small fee, the court records are free with suitable ID & if you explain who you are and why you need the info. I would check these out FIRST before you write anything that could be construed as incriminating on an applicaton. Why make it harder than it already is?
Hope this helps, good luck.