A numbered canvas is flat by design, and the two ways to give it dimension are completely different from each other. One is physical — paint you can feel. The other is optical — the illusion of distance, which is mostly already built into the design and just needs to be painted properly. Depth on a framed canvas is the same argument applied to a piece you intend to hang.
The second is where most of the available improvement is, and it needs no extra materials.

Optical depth: what the design already contains
A good landscape design has distance encoded in it. Your job is to not flatten it.
- Distant things are paler, cooler and lower in contrast. Those pale blue-grey hills look wrong in the pot and are correct on the canvas. Painting them stronger than intended pulls the background forward and kills the depth.
- Value contrast is what creates form. Light against dark does far more for apparent three-dimensionality than color does. Preserve the darks — the instinct to lighten a very dark passage is the most common way people flatten a canvas.
- Warm advances, cool recedes. The foreground is warmer for a reason.
The practical instruction is short: paint what the numbers say, at full strength, including the colors that look odd. The depth appears when the canvas is finished.
Physical texture: how to add it
Acrylic holds a brush mark, and that is the whole basis of physical texture. Three approaches, in order of risk.
Directional strokes. Free, invisible until it is not, and the one to actually do. Brush along the direction the form runs — up a tree trunk, along the roll of a wave, following the plane of a hillside — rather than back and forth. It costs nothing and it adds movement that reads from across a room.
Thicker paint in the foreground. Apply foreground sections a little heavier and background sections thinly and smoothly. The physical difference reinforces the optical one. Keep the difference subtle; heavy build-up at a section edge shows badly.
Dry brushing. Very little paint on a nearly dry brush, dragged lightly over a dry surface. It catches the weave of the canvas and leaves a broken texture — good for foliage, weathered wood, water sparkle. Test it on the canvas edge first, because it is easy to overdo.
What not to do
Texture medium and modelling paste. Sold for exactly this and generally a mistake on a numbered canvas. Applied before painting they bury the printed numbers; applied after they sit on top like a coating. The kit's paint has enough body for anything this format needs.
Palette knife work. Thick knife-applied paint covers section boundaries, and once you cannot see the boundaries you are painting freehand without a plan.
Texture everywhere. Uniform texture across a whole canvas is the same as none — it reads as a rough surface rather than as depth. Texture is only depth when it is selective.
Finishing so the texture shows
Let the canvas cure for several days, then consider a satin varnish. It evens out the patchy sheen from thick and thin passages, which otherwise reads as unevenness rather than as texture.
A gloss varnish deepens the darks more and increases contrast, but it also reflects, and reflections compete with the brushwork you were trying to show. Satin is the safer choice. Test on a corner either way.
Common questions
How do I make a paint by numbers look three-dimensional?
Mostly by painting it as designed — keeping the darks dark and the distant colors pale and cool. The depth is built into the design and is lost by flattening those.
Should I use texture paste or medium?
No. Applied first it hides the numbers; applied afterwards it sits on the surface as a coating. The kit paint has enough body on its own.
Does brush direction matter?
Yes, and it is the best free improvement available. Stroke along the direction of the form rather than back and forth.
Will varnish flatten the texture?
Satin varnish evens the sheen without hiding brush marks. Gloss reflects more and can compete with the texture you are trying to show.