Assuming that your texture image is on the left side and the object you want to apply the texture to is on the right:
Open your object (mesh) for editing. Select all the verts (A) then, from the UV menu, select “Unwrap Angle Based.” You can also just press (U) and select from the menu that pops up.
Go to your UV Editing context (Row of top tabs). You should see a 2-D unwrapped representation of your mesh. (Be sure that your object is still open for editing.) The verts and edges on the UV-unwrapped representation correspond EXACTLY to the verts, edges and faces of your object.
In the menu bar of your UV window, click the “file folder icon” and find the image that you want to map onto your object. It will appear as a layer under your UV Map. You can select, drag and edit the verts of that UV map until they line up the way you want them to. Just do this until things are the way you want them to be.
Go back to your Default Workspace and make a new, blank material then apply it to the object. Judging from the image you posted, I assume that you’ve gotten this far. Yes? 
Now, it’s time to go into your Shading Workspace and hook things all together.
In your Shader Editor you should see a generic layout of your material nodes. There is likely to be a Principled BSDF and an Output node. Again, I’m assuming that you have gotten this far, already, and can find your way around. Right?
Now, it’s time to hook things up! 
- Shift-A to ADD a Input > “UV Map” node. Select the UV Map of your object from the drop-down f it isn’t already selected.
- Shift-A to ADD a Texture > “Image Texture” node. Use the drop-down to find and select the image texture that you want to apply to your object.
- Connect the nodes:
UV Map [UV] ==> Image Texture [Vector] ==> Image Texture [Color] ==> Principled BSDF [Base Color] ==> Principled BSDF [BSDF] ==> Material Output [Surface].
If all goes well, you should have a basic UV Mapped, Image Texture on your object. This is just the basics. Simply, how to put the texture image onto your object. There’s all kinds of other stuff you can do but this should be enough to get you started.
Let us know how you get along, so far. Once you get the first part down, we can talk you through other things you can do to improve your results. 