There is a more modern style of projectile first known as the Minie Ball, used in the US Civil War (1860-65).
Lead balls are not only heavy, but also loses accuracy over distance because its not perfectly round. This method also suffers the same thing without professional equipment, but it looks much more like modern bullets.
This method uses pipe to make the mold. The pipe also becomes part of the round. The end result is various forms of jacketed bullets.
This method allows you to make:
FMJ (Full Metal Jacket)
JHP (Jacketed Hollow Point)
JSP (Jacketed Soft Point)
Semi-AP (somewhat Armor Penetration- depends on core)
Before starting, you will require:
1. Some metal pipe that fits inside your barrel. A sabot method can be used if there is more than 3mm on the sides. Sabot is when the sides of the round is wrapped in another material to ensure a good fit. So even a .50 cal round can fit in a .75 cal barrel. The pipe should have as thin walls as you can find.
2. A way to cut the pipe (like a hacksaw)
3. A hammer or something. adapt as needed depending on what type of equipment you have. I used a hammer, but you can use other stuff if you want to.
4. Lots and lots of lead
5. Someway to melt the lead. At least use a candle or something. Be aware that some leads may contain hazardous substances, such a mercury or other heavy metals that may come out hen the lead is heated. You will need about a 900 degree flame to melt lead.
6. Plaster, clay or just plain mud. Mud needs to be free of rock and needs to be very thick.
7. A large container to fill with water. Make sure the container can actually hold the water and not break. You will need to at the very least submerge an object completely that is the size of a 1L bottle. Get a clay or metal bottom for it.
8. A steel, copper, or alum pot/cup/bowl to melt the lead in. Make sure you're not going to eat from it ever again. Lead sometimes contain some very bad stuff.
9. Pliers, something to move very hot and heavy containers of liquid metal with. Surprisingly, wood doesn't catch on fire easily.
The guide. Its one MS paint pic.

Some info not on the pic:
1. Lead is easy to get. The cheapest way is to reuse anything made of lead that you already bought. Other places to get lead can be your local scrapyard or gunstore feature super cheap shotgun loads or walmart. Lead can be extracted from shotshells by cutting them right thru the wadding.
2. Depending on where your lead is from, you may encounter hazards of trace metals in the lead. Do the whole thing outside. I use lead from real bullets, shot gun shot, and small lead block I find everywhere. My lead sometimes smells very heavily of ammonia. Like I said, do it outside.
3. a candle is the worst way to melt lead. Slow and tricky. If you have a more powerful way, please use that instead. Soldering guns also is a bad choice.
4. Lead can be mixed with other low-melt metals, such as tin. Do not use lead containing flux.
5. chopsticks can be used as handles to hold the hot containers of metal with.
6. Seriously, do not use steel or iron as a core. that makes it an AP round, illegal in almost all areas. It also increase penetration, increasing the chance of getting someone injured or killed.
7. Wax or plastic can also be poured in in place of the lead as a weaker alternative. Weight can be increased by adding some lead shot or large chunks of metals while it is being filled with wax or plastic. Put all metal toward the end or middle of the bullet. It will reduce it becoming shrapnel.
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Its not really a practical way to make bullets. But its the best way if you want maximum power, penetration, and damage.
For some people, this is a very bad idea, because the more powerful the gun is, the more dangerous this type of projectile is. The most powerful all-metal spud guns may end up with more power than the most powerful legal gun you can buy (NFA class 3 not included).
Always be sure of the backstop before shooting.