I have only a small amount of time each week when I can get on the air. Frequently I turn on the radio and hear numerous operators participating in one contest or another. Is there some way to indicate I am not participating in the contest? That I am just getting on the air to rag chew or maybe log a few new DX entities?
If you're asking if adding "/NPC" (for "Not Participating in Contest") to the end of your call sign or something like that will help, then I'm sorry to tell you that there is no commonly-recognized way of designating yourself as someone not interested in making contest QSOs. But don't lose heart, contest activity can be avoided: see "I hate contests. How can I avoid them?" One of the easiest ways to avoid a contest is to head to the "WARC bands": 12m, 17m, and 30m. Contest rules generally don't allow contacts on those bands.
In addition to finding bands, frequencies, or modes where contest activity is not allowed or scarce: If you're answering a CQ, just don't answer a contester's CQ. They're easily distinguished by "CQ contest", "CQ TEST" (on Morse code), or "CQ [contest name]". On the weekend, it helps to know what contests are happening; maybe bookmark a contest calendar like this one in your browser, and learn the names of the major contests, since the major ones are harder to avoid than the smaller ones.
If you're sending CQ, it can't hurt to say "CQ RAGCHEW" on Morse code, or something like "CQ, looking for a ragchew" on phone. In Morse code, sending CQ slowly will strongly discourage most contesters; typical speeds in major contests are 30 WPM+, so 20 WPM or less will make most contest operators who are looking for a QSO want to keep spinning the big knob.
If you're looking for new DX entities, you can of course always call "CQ DX" instead of "CQ contest", although a few clueless contesters might try and work you anyway. (Be kind; some contesters try and operate for 48 hours straight in the big contests, and that kind of fatigue can make one do funny things.)
But you might also consider joining in DX contests, even if you only have a few minutes to spare; lots of semi-rare entities are much easier to get in DX contests, and lots of DXpeditions make a point of planning their operations around the big DX contests. I would highly advise waiting until the last hours of a DX contest, usually Sunday, because contesters calling CQ get much more patient and accommodating toward the end of the contest when their CQs would otherwise go unanswered. Remember, a contester wants every QSO that can possibly be made, even yours. It helps to know the rules of the contest to know what information is passed in the QSO, which is called "the exchange" in the contest rules, but such an accommodating contester will usually be happy to ask you for the information one item at a time. If they ask you for your serial number, just start with 1 for the first contest QSO, 2 for the second, and so on. You are under no obligation to submit an official entry in the contest. It's fine to make just one QSO in a contest, although it's polite to make two or more QSOs if that's not impractical for you.
By the way, most contest stations are very good about confirming the QSO, either by Logbook of the World or by QSL card. The reason is, if a contest station isn't polite about confirming QSOs, then other contest operators will remember and refuse a QSO with the rude operator the next time around, which would hurt the rude operator's efforts in future contests.
If you are calling CQ, then there are a few ways to make sure you don't sound like a contest station.
First, if you are calling CQ:
For SSB, a contest station might call "CQ contest, CQ contest, HS0ZLW CQ contest" or if they are busy, just "HS0ZLW CQ contest". This is sent as quickly as possible while still remaining intelligible. So you just try saying "CQ CQ CQ, HS0ZLW calling CQ CQ 20 metres CQ CQ HS0ZLW calling CQ and standing by" or similar. And you do it at normal pace. Do not mention the word "contest", as a contest operator might glom on to that and think you're calling CQ contest.
For CW, a contest station will be calling at at least 24wpm "CQ HS0ZLW TEST" or just "HS0ZLW TEST" if they are busy. So you call "CQ CQ CQ HS0ZLW HS0ZLW HS0ZLW CQ CQ K" at a slower speed. Contest stations will hear your pace, and not hear TEST at all, and will just go straight past.
Secondly, if you are listening to people to call:
Avoid people calling very quickly "CQ contest", or in CW "TEST". This bit is easy.
Thirdly, how about you mix it up a bit?
12m is a very quiet band at the moment. It's probably the least used of the WARC bands. And the way propagation is at the moment, there's not much to be found there.
17m is an amazing band. I was once scanning around and heard the huge Heard Island DXpedition calling CQ on there in CW with no takers. Worked them first call. There is usually activity on 17m at all times of day and night, as its propagation characteristics are somewhere between those of 20m and 15m.
If you are into CW, then have I got a secret for you! The 30m band is a band with characteristics somewhere between 20m and 40m, and it's not affected too much by the D layer like 40m is, so there is good DX to be found there during the day.
If the main contests of the weekend are focusing on CW or SSB or RTTY, then simply use another mode for those days. Or you can use FT8 or JS8CALL and still have a lot of fun. If you are a CW person, but the CW portions of every band are full of contest stations, then blow the dust off the microphone and give your vocal cords a tryout! Or if you are an SSB person, dust the key off and remind yourself how much fun can be had on CW (even a QRS CW contact can be very rewarding if you are not used to the mode!).
Basically, the contesters are on the bands for a limited time. If you stay out of their way, they will not bother you. It's just another aspect of this fantastic hobby we call ham radio.
[Disclaimer: I used my own callsign as the example in the text above]