Wandlore is a very complex and misunderstood branch of magical study that few can really grasp onto. It may sound simple, and for the experienced wand-maker, it IS simple, however for those just studying for the first time it can really confuse and bewilder. Wands can be made of nearly any material, though most commonly wood. 

I will explain how to make a wooden wand and also how to use wands (any kind)

First, you must find a branch or length of wood you wish to work with. There are MANY types of wood and each lends its own magical properties which can affect the magic (all wands can do ANY kind of magic but it will excell and be 'better' at those aligning with its properties) I will give a BRIEF description of SOME woods but if you are serious about making your own wooden wand I suggest you consult a website or a book that has the sole topic of wandlore and wand making.

Willow- healing, divination, enchantment

Oak- creativity, strength, focus

Elder-Transformation, Manifestation, Exorcism

Poplar-Anything- most diverse wood

Ebony- Manifestation, power, strength, (that extra 'umph' for spells)

Holly- Attraction, Dream Magic, and manifestation

So if you have to get a branch from a living tree, be sure to ask the tree's permission first- once you feel an energy from the tree that feels negative or affirmative then you have your answer. Afterward give the tree an offering such as water, a penny, or a genuine blessing. If you find your wood laying around on the ground or you make it from a dowel that is just as fine. Hold it and let the wand tell you the shape it wants to take. Once it gives you a clear vision, begin whittling to make the basic shape then use wood working tools to add in details and give it more life. sand it down until it is smooth to the touch and then apply any stains you wish, and then a protective wood varnish (do a few coats), and once it is dry you may then have it consecrated, blessed and enchanted. It IS possible to put a magical core into the wand- but this must be done in the astral plane-which CAN be a dangerous realm to visit...

IF you do go to the astral plane and have experience doing so research what attributes magical creatures can give- and then go and ask for that being to enchant the wand with a core. leave an offering. 

Do NOT take something from a DEAD being. Dragon Heartstrings tend to be a common wand core to some wandmakers, but those wands almost always backfire and leave desolation in its tracks. If you take a core from a dead being at best it will have no effect on the wand but most likely will end up corrupting the wand, the magic used with it, and the wizard himself!

Be sure to approach a live being and give an offering- then ask for the favor. 

Once it is done the wand will physically feel a bit different with its energies.

Now with using wands-

hold the wand in your dominant hand for casting spells and projecting energy, and in your non dominant hand for receiving energy. 

you can do many different things with your wand to cast magic.

If you want to manifest something or speed up a process etc wave it clockwise,  if you want to banish something or slow something down wave it counter clockwise. If you want to directly affect something or someone either point it at them or tap it or tap them. (if you cannot see your target or they are far away point in their general direction or straight up in the air, or at a picture of them or it). Write things out in the air with your wand and then give a grand clockwise wave and point upward to attract or manifest what you wrote.  aim at the ground and draw a circle to cast a circle spell. or If you are in a rush and cannot formulate a spell just wave your wand with the strongest desire or emotion you have and watch magic happen!