There are loads of different ways to refinish a stock, and a lot depends on your patience and what you hope to achieve as an end result.
You could do with knowing what the stock is currently finished with, as many Berettas have a "truoil" finish, which looks like a traditional oil finish, but isn't!
If you have plenty of time on your hands, then I would suggest stripping the old finish completely, staining the stock to your taste and then refinishing with a traditional hand-rubbed finish. It'll take several weeks, but as a labour of love it is immensely satisfying. It's fiddly, and initially time-consuming, but the results are worth it.
To get rid of the old finish you need to strip it off using fine grade wire wool, meths and elbow grease. Don't use white spirit or else you'll leave an oily residue in the wood which will cause you problems later. Take all the metal work off the stock, and remove the butt pad or plate. Be very careful when working around wood-to metal areas not to inadvertently remove too much wood which will mean gaps and rounded corners where the wood should butt up to the metal properly. This is especially important if you are sanding in the next couple of stages. Work with the grain, especially if it's a straight grain bit of walnut. Don't use too much effort over the chequering, unless you intend to re-cut it later.
Having stripped the stock down to bare wood, you can now work on any dings or dents. Use a piece of cloth soaked in water over any depressed dents and hold the tip of an iron, set to max, on the cloth directly over the dent. This will drive water/steam from the cloth into the wood fibres and expand them to raise the dent.
Next, gently flat the finish with wet'n'dry, as fine a grade as you can find. As you wet the wood, you'll raise tiny fibres which will be whisked away by the paper. Don't press too hard or else you risk leaving finger grooves in the surface. Once it feels absolutely smooth all over, allow the stock to dry completely before going onto the next stage.
Depending on the colour you want, you'll need to stain the wood. You can buy traditional alkanet root oil stain, which will give a nice deep reddish tint to the dark bits, and an amber appearance to any light bits. Follow the instructions on the bottle, as some compounds differ in use. Generally though, use a piece of soft cloth or cotton wool to swab the stain evenly and sparingly over the stock, working along the grain. Once it's dry, decide whether it's the depth of colour you require, and repeat, using very sparing layers until it's just a bit darker than you want. It'll get a shade lighter as you move through the next stages.
Next stage is to seal the grain. Buy an appropriate grain-sealer compound which is basically a wax containing rottenstone or pumice, and this is rubbed onto the wood to fill any open pores. Again, follow the instructions on the jar, but it needs to be rubbed into the wood, then rubbed off once dry leaving the pores clogged. You could use dry wet'n'dry once this stage is finished to make sure you have removed the wax from the surface. You could also leave this stage out, but if you want a traditional "London" finish the grain needs to be sealed.
Now the oiling stage. You need a proper, traditional Walnut Preparation. This is boiled linseed oil, often with hardeners added. (I once advised someone to use Walnut Oil and they old me it was shite, before I discovered they'd been to Tesco and bought a Walnut Oil salad dressing!!!)
Again, follow any instructions to the letter, but generally speaking you need to clean your hands, and then dab a drop of oil the size of a 1p coin onto your palm. Rub this into the wood, along one side of the stock. Rub quite vigorously (Madam!) as the heat from the friction and your hand drives the oil into the surface. Once you've covered one side, repeat on the other.
Initially the wood will soak the oil in quite quickly, but don't be tempted to rush this stage. If you overdo it and add fresh oil to a layer that's still not dried off, it'll end up sticky and you'll have to wire wool it off and start again. Leave the stock to dry for a day and repeat. As you add layers of oil the finish will start to build. At first it'll dry quite matte, but as you progress it'll start to build a sheen. Do this once a day for a week, then once a week for a month (although to be fair if you can leave it in an airing cupboard to dry it'll be OK after three or four days)
After a few weeks you'll get an idea of how it's going to look. If it's reached a depth of finish you're happy with, then you have a choice. You can either leave it as an oil finish, simply oiling it as above every time you take it out. This way you will eventually build up a beautifully patinated oil finish.
If you like things shiny, you could use a wax finish to give you a pretty, gleaming gun. You could even give it a button polish using wax and rottenstone, if you were that way inclined, or simply use something like Slippery Dick's wax finish.
Have fun.