Nowadays, lay people generally cannot obtain any first class relics through official sources, unless it is a case of the lay person personally obtaining such a relic from the saintly person while s/he was still alive, or maybe receiving it as a gift from some other person who got it while the saintly person was alive. (I’ve heard stories of people who got a fragment of a Padre Pio glove stained with his blood from somebody who knew Padre Pio.) You could possibly find a purported first class relic to buy either from eBay or from a dealer. In such a case, however, there would be a risk of committing simony from engaging in the buying and selling of holy relics.
You might decide to go ahead anyway, perhaps in order to rescue the relic from someone who wouldn’t treat it reverently. I understand this is sometimes an acceptable reason to buy them and at least one major US relic shrine has hundreds of such relics that a rich Catholic priest bought for just this reason. However, the first class relic you received might be a fake even if it had a certificate; the price would probably be very high for a first class relic; and Catholic lay people who have first class relics really aren’t supposed to keep them but instead are supposed to turn them over to the Church, such as give them to your priest.
Regarding second-class relics, they are a little easier to come by. If the person is going through the canonization process, often their cause will send out cards with second-class relics, usually a tiny piece of the person’s clothing. I got one for Fulton Sheen recently, by simply writing to his cause and requesting one and making the suggested donation. If the person is relatively recently deceased, you may be able to buy something like an autographed book of theirs. Also sometimes the saint’s shrines or other people will sell you a reliquary or something and include the relic, and the price for the whole thing is reasonable price for the reliquary, so it’s not simony. The Shrine of St. John Neumann recently was selling paperweights that contained a piece of his coffin, which is a second-class relic, and they were very inexpensive (cost of a normal paperweight), so I bought one.
You can also sometimes obtain second-class relics on eBay or from dealers; again you risk getting into simony if you pay too much so it’s up to your prudential judgment. You don’t have to turn them in to a priest like you do with first-class relics. But really best to obtain them straight from the saint’s shrine or from their official cause to make sure you are getting the real deal.
Edited to add, the St. John Neumann relic paperweight is still available in his shrine’s gift shop here. I would note that when mine was sent to me, whoever mailed it did not calculate the postage correctly so it arrived “Postage Due”.
https://stjohnneumann.org/shop/
Information on how to get the Archbishop Sheen relic card is here (My card had a purple vestment fragment):
http://www.archbishopsheencause.org/the-cause/request-materials