I use a shaving mug, I have several, one bought for me by my wife, the other by my mom, and several different types of soap. I have a badger hair brush (the best IMHO), but the synthetic stuff is still good. If you want to try it out, find your DE safety razor and get some good blades. My favorite is Feather, but they're super sharp. Sharpness differs from brand to brand so you can buy a multi pack like I did for just a few bucks. This will allow you try different blades to find what works best for your face. Some are more aggressive than others. This is an art to me, just like smoking a pipe.
I just toss the block into my mug, run some hot water over it, run a sink full of hot water and place my brush and razor (fully equipped with a blade....actually forgot to put one in one time and "shaved" half my face before realizing), then I make sure I soak my whiskers with as hot a water as I can stand. It makes the hairs stand up and allows for a better shave.
Now each person is different, I've done it with and without it, but pre-shave oil on your face prior to applying the soap can prevent the razor from causing any discomfort on those first few attempts, because you might have a learning curve in keeping the proper angle, but you'll get it. The oil can just help, but is not required.
Then shake some of the water out of the brush, not too wet, not too dry, and then put it on that soap and work up a good lather. Apply it nice and warm to your face and work it in against the grain. Really work it in because those bristles will stimulate your skin and also provide some exfoliation. Sounds un-manish, but sometimes it's just good for the skin.
Now you're ready to shave, and as directed above, NEVER shave an area without lather. If you need to re-shave an areas, reapply after you've made a first pass. I require at least two passes every time, just because my beard is so thick. Once with the open comb, then again with my tech razor to get the smooth shave result. Always shave with the grain, not against it is the rule, but I HAVE to shave against the grain in some areas to get a fully smooth shave.
Wipe up, clean up all the puddles and piles of soap and whiskers, then apply your favorite after shave. I heavily suggest non-alcohol versions unless you're skin is used to it, or you'll be screaming in the mirror like Macaulay Culkin. If you don't mind a little burn, I heavily recommend Bay Rum...my wife could eat me up after I use it. Also, in the inevitable event that you nick yourself, very cold water on a towel can stop your bleeding, or, you could always buy an alum block or styptic pencil. They burn a little, but help stave off that nick and stop the bleeding so you're not running around the house with tiny pieces of bloody toilet tissue stuck to your face or spotting up your favorite dress shirt.
In addition, please make sure you wash out that brush, buy or get a cheap stand combo if you can, Walmart sells a pretty awesome little package of bowl, brush and stand pretty cheaply. Now once you're done, also take apart that razor, wash out the scum, hair and soap, dry it off, and dry that blade carefully. This will ensure you don't collect any rust or buildup that hampers your shave. It builds over time if you don't do this and you won't have nearly as nice a shave. A double edge safety razor is a tool, an instrument of facial artwork, if you will, and when taken care of, will last you a lifetime.
I always shopped primarily with
West Coast Shaving and really liked their wares. You can get everything you want/need from them for really good prices.
Forgive the super long post, but I do so dearly love the art of shaving and my razor collection. It's right up there with pipe smoking for me.