Whether you choose to do so or not, before you can play you'll need to start building a deck. The easiest and most popular way to do so is by looking them up on the internet. If you search for zero-cost decks you'll get a wide selection that you can play with your Basic cards alone.
Most feature ones you haven't unlocked yet, so you'll need to pick some replacements. Plus you may have opened some cards that you're itching to play with. This is where the fun begins. At the highest level most players copy or tweak the most powerful archetypes. But at the bottom of the ladder, you're free to experiement.
The art of deck building is much more subtle than shoving in all the most powerful cards you've got. For example, let's take the Legendary dragon Malygos, one of the possible and most desirable cards you can get from that welcome bundle.
It gives all your spells +5 damage, but it costs 8 mana. If you play it, your opponent will try and remove it as soon as possible. So, ideally you want it in a deck with some 1 mana, low-damage spells. That way you can play two on the same turn as Malygos for maximum pain.
But wait, there's more. You might also want to hedge your bets and try to keep Malygos alive as long as possible. That means defending against minions and offensive spells.
Other alternatives, out of the reach of new players, are getting more mana crystals for a turn or copying Malygos or making it cheaper. And doing any of these things requires you have plenty of cards in your hand, which means you need card draw.
Taking all this into consideration you can see how you can begin to build a deck around Malygos. And if you look at the top level deck Malygos Druid, you'll see it has all these ingredients already in place.
But expensive decks like that are for the future. Right now, take a zero-cost deck as a starting point and think how the cards you've collected might fit into it. How the various cards and powers work together will come with experience, but do your best to plan in advance.
What if, for example, you've been lucky enough to find the ever-useful Knife Juggler in a pack? He's an easy inclusion in starter decks heavy with small minions, like those for Shaman, Paladin or Warlock. But he'll do poorly in minion-light classes such as Mage or Rogue.