Three-Star demotion is a double-edged sword which lessens the levels of the monster from your hand by 3 at the huge cost of 3,000 Life Points. It's less used now since the skill re-balancing, but it could still be deadly especially when paired with Double Summon. Maximize its effect by summoning 2 high level monsters at the turn when it's activated. Just make sure that you have a clear advantage upon using it, since the drawback might cost you the game.
Champion's Vigilance currently is the only card in the game that can negate a summon. By preventing your opponent's summon, you can attack directly on the next turn if he/she has no monsters. You can start using this once Dark Magician is on your field. It can also negate spell/trap activation, which is very good on disrupting your opponent's combos. Just pay attention to your opponent's moves and don't use it on impulse, they might bait you to use this card before doing their true combinations. Being knowledgeable about other decks would greatly help.
Very good when the duel drags out since it heals you over time. Also clogs your back row.
Getting Dark Magician
Using the 2 search cards, you can get them from either your deck or graveyard to your hand. If you get first turn, it's best to use these 2 to get more to your hand, thinning your deck and getting multiple copies. You can make the best use out of a single skill activation that costs 2,000 LP by using Double Summon and get both DM on the same turn.
Barrel Dragon or Dark Magician
The starting hand often will determine which one is better to summon. If you have a Champion's Vigilance, you can summon DM and wait a turn so that it's ready to use on the next. Summon Barrel Dragon when you don't have anything that you can use. It's recommended to play it more safe and attack when you are certain. If your monster is destroyed, it can be hard to make a comeback when you can't recover your LP to activate the skill again. If your opponent has multiple spell/trap cards, it could be Order to Charge or Mirror Wall. Activate Barrel Dragon's ability each turn and don't attack into a attack position monster if you are not certain.
Dark Magician Girl
Instead of Barrel Dragon, you can use DMG together with Sage Stone and make it more spellcaster oriented. Summoning DM might be easier, but DMG has lower attack, defense, and less useful effect.
If you find that the deck is lacking some draw power, you can use cards like Crystal Seer, or Jar of Greed so you can get the ones you need faster.
Other normal monsters
Instead of only using Champion's Vigilance for DM, you can bring more normal monsters, or exchange them with Barrel Dragon. This will make it more normal monster oriented, but it can still work since they have their own supports as well as searchable with Legion the Fiend Jester, or Blue Dragon Summoner.
That's the issue I see with DM in Duel Links given the short number of cards. DM decks, in contrast to BEWD, for example, are heavily depended on various Spell combinations in order to make it work, unless you summon DM immediately. So this deck just doesn't work if you're unlucky.
Yeah but with masoleum you need to draw the field spell first, so it's a little bit incosistent, unless you dedicate your deck to search it.
I really don't understand why people complain so much over those skills, the only thing i hated so far is the fact you can have only one structure pack for gems, rest is about p2w, so gives an unfair vantage to those who pay, despite that, konami is doing a good job