Ahhh walnut!
A beautiful wood that can be finished in many ways.
It must be treated with some forethought to bring out the best.
While there has been posted many different methods, I will relate what has worked for me for the last 50 + years of fooling with
First, the surface prep is majorly important to the final look.
Sand the wood down thru successive grits to remove previous scratches.
Lightly wet to whisker the grain. Sand it flush with the last grit used. Repeat as necessary til you no longer raise any whiskers...
Now the beauty part happens.
Using the stain of your choice, be it alkanet root based or an aniline dye available from TOTW apply sparingly at first. Keeping in mind it may look a bit light or dark initially.
Fear not, it will darken up a bit more when the sealant and finish goes on.
Let dry completely. Sand any raised grain off.
Sealant such as Permalyn as developed by John Bivens goes on next. It penetrates the wood and seals it from moisture.
Coat the wood until it doesn't absorb any more and shows wet on the surface after a few minutes. Wipe the remainder off and set aside to dry and harden for a few days.
It's supremely important to let any finish completely dry before adding more.
Now lightly sand the surface with 320-400 grit to fill the pores using bpiled linseed oil or your preferred finish to produce a slurry that you will let set up. Then, when dry sand back flush to the surface. When the pores are filled you are ready for the final finish. A quick side note...to pop the grain even more you can use a dark wood dust to sand into the pores for more contrast. Ebony works very well.
The finish you use is also an important choice.
Boiled linseed oil with a japan hardener such as Tru-oil can be applied and when dry struck down to the sheen desired. The modified oil developed by Bivens can also be used in a similar fashion.
A note about tung oil is relevant. Tung oil can cause dermatitis in 10-15 % of folks with sensitive skin.
Something to keep in mind.
Continue on to the desired look you like.
Good luck!
Some examples of stocks finished by the methods I've described.
Enjoy!