Check it yourself! Do an image search for treasure chest. Select a few good ones. You'll see to match with them you must insert:
- a lock
- edge and surface reinforcements
- carrying handles
- material texture details
- a treasure, if your chest happens to be open, maybe also the hinges are partially visible in this case
- lights, shadows and maybe some shine
- plausible colors.
As a practice job you can well try to copy one. I do not mean copying and pasting, but drawing. It's useful for your learning. Remember to make your own version if you are going to give or show it to others.
The extrusion gave to you so little part of the needed things that as well you can draw the chest with the pen. I bet it's 500% more useful for your learning.
If you happen to wait for the missing things something as easy as the extruding is for the base chest body shape, you will miss it totally. You must draw them or copy clipart shapes.
I see parts of the treasure and wood texture could well be taken from clipart. I bet you as soon draw the metal parts of the chest as you adapt some existing parts exactly to the geometry.
NOTE: It's not plagiarism nor otherwise criminal to use clipart components if the clipart really is free to use with no limitations or you have purchased a valid license to use them.
My opinion is: Use clipart only if you are in a hurry. Remember to admit there's clipart parts included, never stay silent and let others think you have created it all.
About HOW?
You have 2 major options. One way is to map detail & texture images (=drawings, photos) onto surfaces. The mapping dialog opens with the Map Art button. It will be tricky if you try to insert also parts which have substantial thickness. The images must be dragged to the symbols panel before use. You must have a complete and fitting image for every visible surface. The curved surface is virtually impossible case if the extruded curve had more than 2 anchor points. It seems to be an ellipse. It has one too much, but you could fix it easily.
Generally you should not extrude curves, but filled areas without stroke. The number of surfaces would be reduced 50%. Do not use black, but light grey.
I bet for future works it's useful to draw in 2D. You can use extrusion to get right viewing direction and perspective with low effort, but expand it to 2D as soon as possible. An example:
the gable shapes NO STROKES!
Extruded, no shading, a slight perspective
Object > Expand appearance is applied, several ungroups to ungroup all,fill colors are removes, all generated shapes have got different stroke to show them. Generally they will be quite surprising and difficult to use as is
Areas are combined and filled with separate colors to get easy to use shapes. The shape builder tool does the job perfectly. Only four separate shapes are left.
The next step is to draw the details. You can make a copy, remove the fills, insert a stroke and split the parts with scissors to get well directed lines and curves to reduce actual drawing:
A splitted copy as material storage
Reinforcing iron edges are placed to the chest body. They are stretched by dragging with Shift key pressed. The extras do not harm, they are easily deleted after applying the shape builder. I used only straight lines, but this is the first place where a little imagination and some curves would make a big difference.
Iron areas are filled with the shape builder, the black remnants are removed, slight strokes are added to show the borders. Also a gradient is applied to show you do not need it from the extrusion.
Here's an example of using curved shapes instead of straight lines. This is actually my 2nd attempt. The projection is a little lower to make the walls of the chest body apparently bigger.
The iron shapes are drawn straight on the face and forced to right forms with envelope distortion. Magenta shapes are copies of the chest walls. They are the top objects in Object > Envelope distortion > Make with Top Object
This show ends here. Hopefully you got some ideas. You need also actual drawing and you must place surface textures. Those details are beyond the scope of this answer.