Before you make a trellis, be sure to know the difference between a trailing plant and a vining plant, or a vining plant and a bushing plant.
Trailing plants want to grow downwards or creep along the ground. Burrow’s tail-type succulents, Pilea depressa (baby’s tears pilea), Maranta prayer plants and strawberry begonias (Saxifraga stolonifera) are all trailing plants and do not do well when stacked up or trellised. They are better either trimmed or guided to the ground. You can guide these plants to the ground by letting them hang and do their thing. You can trim or prune lightly, but if a severe trim is needed, you can trim all growth to about an inch or two over the pot’s edge. There should be enough of the plant left behind to have enough nodes to branch out and trail some more. If you have a significant chunk of plant leftover, you can attempt to plant them in the soil, but this will only work for either succulents or for plants with little rootlets on them.
Vining plants enjoy growing upwards and are semi epiphytic. Most houseplant vines include herbaceous aroids like Philodendrons or Pothos Plants. You can train them any way you like. You can tie them to a stake or to a wall or just have them creep up your furniture. Loosely tie the plant to a stake with twine or secure the vines with clips. Don’t clip or tie the vine too tightly—make sure that there’s room for the vine to expand. As the vine expands, you may need to adjust and re-tie or re-clip. You can also take the twine and tie the vines to hooks or nails in the wall—anything that is sturdy and can bear the weight of the growing vine. You can train it to grow along a framework or trellis, so long as you tie up the pliable new growth in the direction you want it to grow. Will it grow straight? Not a chance, but it will grow in the general direction that you’ve chosen.
Monsteras are something between a vining plant and a bushing plant. Part of the reason why they’re called monsteras is because they’re monstrous, growing in all directions as a part vine, part bush plant. You can trellis a monstera, but take extra care when handling the vines and make sure whatever you’re tying it to or training it on is sturdy enough to hold the weight. Like any aroid, you can repot your monstera cuttings into moist soil, so long as there is a part of the stem attached. If the plant falls, that’s ok. In nature, vines fall all the time! You can always prop them back up.