Depending on what food you are trying to imbue with a smoky flavour, you have multiple options. I here focus on methods that will just give you a smoke flavour, rather than smoked ingredients.

• Actually smoking the food seems an obvious suggestion. The internet will suggest any number of ways to set up a smoker at home, although you might not want to go through the effort or have to deal with the smoke.
• Cold smoking is often done with cured meats and fish. As the name suggests, this is smoking (actual smoke from actual fire), but without the heat, often accomplished by creating some distance between the fire and the food, and having the smoke travel from the former to the latter. This guide seems quite comprehensive, including some ideas for a home setup. Cold smoking has similar drawbacks to hot smoking.
• Some companies make 'smoke guns' such as this one by Breville/Sage, that accomplish the idea of a cold smoker on a much smaller scale. Thus, no need for elaborate setups, nor the risk of smoking up your whole house.
• Finally, you can look for ingredients or additives that give you a smoky flavour. Liquid smoke is reasonably common. I have also seen powdered versions of this.

In addition to the other good answers, I would add that a lot of the smokey flavour in Mexican foods comes from the chili varieties used.

A good variety for smokey flavour is Ancho (dried Poblano), which are very mild, but have a delightful smokiness to them. They are a key ingredient in some of the very popular sauces like Adobo and enchilada sauce. I think some of the smokiness comes from the drying process, which may include smoking, so substituting fresh poblano will not work

A (much) hotter smokey flavour is provided by Chipotle, which is dried and smoked jalapeno and is also commonly used in Adobo sauce. This one is most likely too spicy for what you want, but is certainly a nice smokey flavour.

Good quality mild/sweet smoked paprika does have quite a smoky flavour. Pimentón de la Vera is a Spanish variety that's reliable whatever the brand (dulce is what you want, not picante).

Adding some cumin helps bring out the smoky flavour, though the flavour of cumin isn't exactly smoky.

If that's not enough, and using more gives too much of a paprika flavour, smoked garlic is a good addition. Smoked onions should be good but I can't buy them and have never got round to making them.

I distill my own whisky (it's legal here in New Zealand). Occasionally if I want a really nice smoky flavour to the endproduct and I can't be bothered with actually smoking oak pieces, and I cheat a little bit instead - I add a few teabags of a chinese tea (Lapsang Souchong tea), which is basically liquid smoke in a tea bag. You may be able to use that idea for your cooking as well.

Another additive that I don't see mentioned much is smoked salt. Obviously it will add salt to a dish, but it capable of delivering quite a bit of smokey flavor.

I have some that my sister in law gave me as a gift in a ziploc freezer bag and the smoke smell was so strong that I had to put it in a mason jar as well. Very, very smokey.

Caramelizing sugars will give you a nice smoky flavour, but you have to watch it every second or you just get burnt. I soak raisins in juice (peach, apple, tomato) plus vinegar and cook them over low heat until they start browning and dissolving. It produces a rich smoky taste perfect for BBQ sauce. Just add more tomato paste for body and you have an amazing condiment for any type of meat - or to give tofu and the like a convincing grilled flavour.

Molasses / Maple

Molasses and real maple syrup each add a depth of flavor that can enhance smoky flavors. While neither alone achieves the effect you want, adding either may help you along to your goal.

A little goes a long way, if you want the flavor enhancement without much sweetness.

You will find various barbecue sauce recipes contain either of these ingredients.

For maple syrup, you would want to use the darker grades.

It turns out that smoke is partially a liquid a room temperature. Alton Brown even did a segment on liquid smoke on Good Eats: https://youtu.be/R3JetOoEngs?t=544.

After seeing that I've been using liquid smoke in a lot of food. Most of them are not made of fake plastic chemicals. They're made from smoke that's been cooled off.

Also, this is how most BBQ sauces get their smokey flavor. They literally pour in liquid smoke.

If you want to know how they make the BBQ flavour (of which smoke is an ingredient of), you can watch this episode of a dutch television program which investigates these things: https://www.youtube.com/watch?v=MuZkmPStZv4

You could try to use auto generated subtitles, I don't think there are English variants, so sorry for that.