Warning: Strong bases can turn your fat into soap. Even if you want to lose weight, do not apply strong bases to your skin. Ammonia vapors are somewhat toxic. They rise in air, so always keep an ammonia bottle on a high shelf.
There are two alkalis used in the home lab: a strong alkali and ammonia. That strong alkali can be sodium, lithium, or potassium hydroxide. There are several ways to obtain these alkalis.
For ammonia: Just buy it. It is very cheap. Always buy unscented ammonia. If you feel like making ammonia, heat an ammonium salt with a base and absorb the ammonia gas in water. You may also want to distil the household ammonia to produce concentrated ammonia.
For lithium hydroxide: Take apart a AA or coin cell lithium battery and add water on the lithium. A white water-soluble solid will be formed, along with some choking fumes. Either keep the white solid in a sealed container and use it when needed, or dissolve it in water and keep that solution in a sealed container for use when needed. If it comes out of solution after being in solution for a few days, it is absorbing carbon dioxide from the air around your unsealed containre. Now it is lithium carbonate, which is not an alkali. Keep it sealed! Lithium hydroxide is used to absorb carbon dioxide in space ships.
For sodium hydroxide: Obtain drain cleaner or oven cleaner that contains sodium hydroxide. Some drain cleaners also contain aluminium particles, so be careful with your choice. The chloralkali process (seen here) can be used to make sodium hydroxide solution. It can also be bought from soap-making suppliers. Sodium hydroxide can also be made by adding calcium hydroxide to a sodium carbonate solution until the solution (not the precipitate) no longer fizzes when vinegar is added. Filter and keep the solution. Keep it out of air to prevent conversion to sodium carbonate.
For potassium hydroxide: Open all of your dead alkaline batteries and pour the contents into water. The potassium hydroxide electrolyte will leach into the water. Since potassium hydroxide has a strong attraction for water, you can keep adding battery powder to your solution, filtering, adding more battery powder, filtering, etc. Do not keep the potassium hydroxide solution in air for any length of time, or it will convert to potassium carbonate. Potassium hydroxide is deliquescent, so it is best to leave it in solution.
Although calcium hydroxide is not an alkali, it is used to make alkalis. For small amounts of calcium hydroxide, purchase pickling lime from the grocery store. For large amounts, purchage quicklime used to sweeten soil. This is actually calcium oxide. If it gets hot when it is mixed with water, it is calcium oxide. Adding water to calcium oxide produces calcium hydroxide, which is known as slaked lime.
This is lithium hydroxide produced by the Li-water reaction. It is stored in a closed container.
Lithium from a CR2450 battery after reacting with water.
I used LiOH for concentrated alkali procedures as my KOH had turned to K2CO3 before I knew to keep it in a closed container. Dilute NaOH solution from the chloralkali process was also available.