Find a branch that splits out kind of evenly into three twigs. Take some clay and mould a kind of nest in amongst the branches. Don't clean up the clay first, this is crude pot and you don't want it to crack, so the little bits of debris and grit are actually good things.
Gather resin and dried moss, add scraps of wax, if you have some, and fill the nest with these. Light torch and it works fine. Eventually the wood burns but the resin and wax flares quite effectively for some time
It's a lot safer, especially if you're going to move it around, with a bit of chicken wire wrapped around the outside of the clay and moss nest; just makes sure it stays on the branch.
Fat and oil runs far too easily. Resin and tar runs but will soak into the moss, or scraps of rags, and burn there rather than dripping. If you do it traditionally it was two sticks, or a small bunch, the original faggot, held together with the cloth and resin trapped in the middle.
There is another way, again with the faggot of rods, but willow or elder this time. Poke down the pith in a handful of rods and pack the opened cores with resin or wax. Bind the rods together into a torch and wrap around the top near the edge with a bit of linen. Dip the tops into resin or tar and light. It's effectively lots of small candles all burning together and it gets very hot.
Modern torches use kevlar soaked in petrol derivatives, like paraffin, or the firegels.
If you look up fire poi you'll find all sorts of suggestions.
Be safe
M