I bought it two years ago, it gives me problems sometimes but I managed it somehow. A week ago, it stopped charging and I don't know what to do. Can someone suggest to me some tips?
Please remember - "I don't want to spend money on this"
Just a shot in the dark ...

The other day I went to charge my Fire tablet, and got a message like "your charger is wet, charging has stopped". I tried plugging/unplugging several times and it didn't help. I tried different chargers (I only have 1 usb-c cable) and it eventually started charging. I switched back to the original charger and it started charging fine.

You say Kindle Fire, so it is an old device?

Good luck.
Try a NEW Cord
Try a different charger and cable
Is it a Kindle Fire (really old) or is it a Fire?
A spray against oxidation may help.
You asked about a 'Kindle Fire'. Did you mean that literally? If so, that is a tablet and not an e-reader, and its a pretty old device.

The first thing you should do is try a different charger and a different cable. Cables in particular have very small wires that have to withstand repeated flexing, so their life expectancy is finite.

Next, you should try cleaning the charging port. Use a new, soft-bristle toothbrush - - - DRY, not wet - - - to carefully remove any accumulated dust or lint.

Has something dramatic happened to your Kindle - like getting soaked or dropped? If the device has been exposed to physical stress, it may have been damaged. In that case, you may need to start thinking about a replacement.

It is possible that you have reached the end of life on your battery (especially if it is a Kindle Fire tablet because that's a old device). Batteries in phones, tablets, and e-readers are designed for a certain number of charge-recharge cycles, and if you use your device a lot, you may have reached that limit. Apple is pretty good about publicizing the number of cycles they design for, but other manufacturers rarely talk about that parameter.

But in addition, the output of many (most) manufacturing processes is typically pretty good, but the fact is that sometimes individual products don't meet design expectations. Some are better than expected, and some are worse. Usually, this is a tiny fraction of the total output of the process, but if you happen to get one of those defective products, it's a big deal for you. It's possible, although unlikely, that your device came with a weak battery.

Amazon's official position is that the battery in their devices isn't replaceable, but it is possible to buy replacement batteries. In fact, there is one manufacturer of batteries who has even posted a YouTube video illustrating how to disassemble an Amazon tablet to replace the battery.

If all else fails, look into Amazon's trade in policy.
Look at your charging port closely with a flashlight and a magnifying glass. I have seen some - usually on phones that are kept in a pocket - so full of lint and grunge that the charger could not make a good connection. This even happened to my phone personally.

If your charging port is grunged, you can clean it out with a sharp toothpick. The plastic ones are generally thinner than the wooden ones. If that's still too big to get in there, you could use a very small straight pin or needle. Yes, you really shouldn't be sticking metal down in there with the contacts, but you are probably not going to do any damage because it is a power input, not a power output. What are you going to do instead? You have to clean it out somehow. Maybe you could break off a plastic bristle from a toothbrush or a paint brush to use as your cleaning tool. Think creatively!

p.s. - In the case of my phone, the lint in my port was not covering the actual charging contacts. It was packed down at the bottom of the socket, which prevented the charger plug from inserting fully to make a strong connection to those contacts. The only symptom there was a problem was that the charger cord did not seem to plug in as securely as it had in the past. But it still felt mostly secure, and the problem crept up so slowly that I didn't notice an abrupt change in how secure the charger plug felt. So I must have gotten used to that slightly unsecure feel as I plugged it in every night. But after cleaning out the charger port, it was very obvious, "Oh, this charger cord plugs in much more firmly now!"

This post raises an excellent point - lint/dust in the charging port is a strong candidate for why a device won't charge properly.

That said, sticking a toothpick or pin into the charging port is a very bad idea and can cause irreparable harm to the device. A far better suggestion is to use a new, dry soft toothbrush.
Agreed. Mine was packed in there so tightly that the softer cleaning implements didn't do the trick when I tried them. It's certainly preferable to have the dexterity and steadiness of a surgeon if you decide to go in there with a hard utensil. I did not find it difficult (I'm not a surgeon!), but some might. I used a headlamp and parked the side of my hand on the phone for steadiness when I was working.

I did not think of a toothbrush until after I had gotten mine cleaned out. The implement I tried first (that didn't work) was a plastic bristle that I cut off from one of those dusting attachments that you put on the end of a vacuum cleaner tube. You don't want to use an actual vacuum cleaner or anything attached to one - those are huge static electricity generators and shouldn't get anywhere near electronic components.