Most of the time, a simple conversation is all that's necessary:
"Is your mother Jewish? Is your grandmother Jewish?"I exaggerate, but you get the point. Often, a simple question is all that is needed to establish "qualifying" for something Jewish, like being counted in a minyan or signing up for a class.
"Excellent! Please marry my daughter!"
But sometimes that's not enough...
From New York Times Magazine:
The traditional willingness to trust a person who said he was Jewish, Ehrentreu asserts, presumed that no one had anything to gain by it. Today, he told me, there are ulterior motives — to be able to leave another country and come to Israel, “to be recognized here as Jewish, to be able to get married.” That is, Israel’s prosperity, its attractiveness to immigrants, is now a reason for doubt.
In some ways, being a convert can make the "are you Jewish?" conversation much easier and streamlined. You have paperwork that says "So-and-so is Jewish." Of course, whether someone accepts those papers as a legitimate proof of Jewishness is a different question. If your mother or maternal grandmother converted, you need those papers. You may also have this kind of letter if you were adopted but born of a Jewish mother.
However, even paperwork isn't a given if you lose it or it gets destroyed. Scan it, copy it, place an original in a safe deposit box, do what you need to do. I can't forget a story I heard online of a man with 4 conversions: reform, conservative, orthodox, and geirus l'chumrah because the office building of the orthodox conversion burned down and lost his paperwork!
When it comes to proving Jewishness, things aren't as easy for born Jews, especially those whose ancestors fled Europe around WWII. So what can you do if you need to prove you're Jewish?
Ideally, your parents have a ketubah. Or your maternal grandmother has a ketubah. If not, you provide a letter from an orthodox rabbi who knew both your maternal grandmother and mother and you. These are the Holy Grails of Jewishness. Of course, nothing is guaranteed in today's political rabbinics climate.
If you aren't that lucky, start with your birth certificate and work backward. Document everything, as more proof is always better. And you never know when you may need to re-prove your Jewishness (yes, really). Make backups of your proof and store them in various places, including the cloud (with appropriate identify theft safeguards). Your birth certificate will be the key to begin proving to governments that you are a family member who has the right to request the record of others.
On the bright side, you only need to focus on your maternal side. If you find proof of paternal Jews, it's good circumstantial evidence but not conclusive. I recommend keeping it, but don't spend much time there.
Ancestry.com is really a great tool to use. It will be worth a membership for a month or two while you sort this out. While not conclusive, you can add weight to your argument with a maternal Ashkenazi heritage shown through genetic tests by Ancestry and 23andMe.
Speaking of inconclusive evidence, it's possible that you may never be able to "conclusively" prove your Jewishness. However, you may collect enough circumstantial evidence to convince a beit din to declare you Jewish. If you're in this situation, I recommend getting a ruling from a beit din on your Jewishness, which will give you paperwork and simplify the question for the future (assuming your future circumstances recognize the validity of the beit din you went to). For example, the Beit Din of America does halachic status determinations.
If your proof is too circumstantial, you may be asked to undergo a geirus l'chumrah, a conversion in case of doubt. What is required for a geirus l'chumrah depends on you, the strength of your proof, and your beit din. It may be a formality or you may have to go through a full conversion process. Alternatively, a beit din could find you Jewish, but "not Jewish enough" to marry a cohen. You could find a rabbi willing to marry you to a cohen, but it might be a headache. However, your children should be able to marry cohanim if you continue to live an observant life and stay embedded in the community.
Back to looking for proof...
Start with the state government, if your maternal ancestors were born in the United States. You should be able to request copies of birth, death, and marriage certificates (you don't need death certificates - but if it's all you have, it's all you have). You can check census records to verify your relatives' residences, especially if they have common names. If your maternal line is in the United States, you can try contacting the local synagogues where they lived to see if old synagogue records exist that list them in the membership. Even better, if their gravestone is in the local Jewish cemetery. Get pictures, many of which can be found online (or requested online through websites like BillionGraves).
Look at whether their addresses were in known Jewish neighborhoods. Do you have family heirlooms that are Jewish ritual objects? Do family members have recognizably Jewish names like Yaakov or Shaindel? Did you find record or family lore of any Hebrew names? Do you have family stories that are clearly Jewish? If anyone is still alive who knew the known-Jew, have them write a letter. Is a different branch from the same female relative living actively as Jews today? Again, see if you can get a letter. Even a secular/government marriage certificate can be useful if it lists a rabbi as the officiant. All of this info can help you.
Immigration records can be key to locating your family's overseas origins. Be aware that immigration documents are notorious for misspellings or even complete misunderstandings. Depending on where your family comes from, that will determine your next steps. Generally, you will be looking for records of burial in Jewish cemeteries, presence on a known list of Holocaust victims, synagogue membership records, or ketubot (marriage contracts/Jewish marriage certificates).
It sounds counterintuitive, but the Mormon Church has the largest ancestry databases and resources, and they are free to the public. If you have problems finding information, your local Mormon Church might be the next best stop. Also check out these resources from About.com's Genealogy website.
It's a good question how far back you can go and still be recognized as Jewish by the community. You may be able to prove that your great-great-great-grandmother was Jewish, but everyone since then has been Catholic. Will you be required to have a geirus l'chumrah? Probably, if for no reason other than simplification (or because of doubt that maybe you can conclusively prove things that far back). However, if you're dating a kohen, this may not be a good answer. If you find yourself in that situation, I don't envy you.
Some stories about the effort to prove one is "Jewish enough" to be married in Israel:
How Do You Prove You're a Jew?
You're Jewish? - Prove it!
So You Think You Are Jewish Enough for an Israeli Wedding? Prove it!
A Ruinous Monopoly