You have 8 minions and 22 spells. That isn't going to work. In my experience, you need at least 15 minions, or spells that summon a minion like the Panther. If your hand is full of spells you are going to lose. You need to play minions because they have the potential to deal damage multiple times. If you don't play minions early, then your opponent on turns 6, 7, and 8 will have all their Hex and Poly and Siphon Soul ready to go when you finally throw down something scary.
You should start at which spells are best in most situations and go from there:
2 x Swipe
2 x Wrath
2 x Claw or 2 x Bite or some mix
2 x Starfire
1 or 2 Starfall
Pretty much every Druid deck has those cards, they are all very nice. I personally don't rely on Wrath for card draw unless it is to pop a Divine Shield. If something needs just one more damage, 95% of the time I will just use my hero power and save Wrath.
Power of the Wild - again, you have only 8 minions to buff, but you have 2 buff cards in your deck. Drop to 1 at best and replace with a minion.
Savagery - very bad unless used with Bite. So you have to have Bite in your hand at the same time, and there must be 2 targets or 1 huge one on the field to make this efficient. The chance of this being a good play is very low. I would only use this card if I was loaded with 2 x Bite, 2 x Claw, and a Savage Roar. But Swipe, Wrath, and Starfire are good enough. This just loads your hand with too many spells.
Innervate, Wild Growth - these are great if you like being risky. You need a fallback plan though. In your case, if you don't draw them early, you have no minions to play so that is your biggest problem. Innervate on turn 1 is great - but you have no 3 cost minions! I prefer a more predictable type of play and don't use either of these cards.
Naturalize, Keeper of the Grove - You either need to add an Owl, a Spellbreaker, or another Keeper of the Grove, because if the opponent gets something on turn 3-5 that you need to silence, you need to double your odds of having silence available in your hand. Naturalize is a good card but only if you are late game and have no other options. Relying on it early or mid-game is going to make you lose.
Mark of Nature, Healing Touch - very situational and I have never gotten much from them. The heal can definitely save you from time to time but again, I would rather play more minions.
Soul of the Forest - extremely good card, if you mass minions. I have a deck that just masses minions in combination with all the ones that summon, like Razorfen. If Soul of the Forest or Frostwolf Warlord is in my hand, it is tough to stop. But this is useless to you because you are not massing minions. You want to cast it when you have 3+ minions on the field.
Force of Nature - very handy to have most of the time, and combos extremely well with a few cards (Cult Master, Soul of the Forest, Roar). If you try to save it for the very late game, it could cause you to lose ground in the mid-game, so don't get greedy and just use it when it gives you what you need.
Ancient of Lore, Ancient of War, Cenarius - 1 of each is great if you have them.
2 big trees - 2 is too many I think. When I have too many big creatures there is always 1 stuck in my hand for many turns, causing problems. I would drop to 1.
So that leaves you with:
2 x Swipe, 2 x Starfire, 1 x Starfall, 1 x Naturalize, 2 x Wrath, 2 x (Claw/Bite), 1 x Force of Nature
1 x Ironbark, 1 x AoW, 1 x AoL, 1 x Cenarius
1 x KotG, 1 x DotC, 1 Panther
That leaves 12 cards and you need a lot of minions to fill this out. Add:
2-3 two cost minions. I like the Panther because if I get it on turn 2 I can summon a minion, and on turn 8 when I have a few minions out, the buff can be very useful or I can just summon another Panther. I also like the Fairy Dragon because on turn 2 the only spell that can kill it is Claw or something lucky like Mad Bomber or Arcane Missiles or an early weapon. I also run 2 Oozes because I hate weapons but that is up to you. I think I currently use 2 Panthers, 1 Fairy, and 2 Oozes as 2 cost minions but it changes.
1 silence minion, either a KotG, an Owl, or a Spellbreaker.
2-4 three cost minions, like Harvest Golem, Imp Master, Demolisher, Shattered Sun Cleric, anything decent since you have none.
2-3 four cost minions, like Yeti, Cult Master, Defender of Argus, Gnomish Inventor, Dwarf, Panda.
1 more big minion. DotC is great, or you can add something else like a legendary that you have.
Some card draw - you have 2 Starfire and 1 AoL. Wrath I don't count. So you will need a few more cards to help draw more. I like the Cult Master but I try to only play him when I am assured to draw something. When he is killed, it is usually with extreme violence because he is hiding behind my DotC - often the opponent will hex/poly/fireball the guy just to get rid of him. That's fine because my AoW or big tree have a bigger chance to survive then if they are wasting hex early. Nourish is good late game so you can keep that in your deck to help with this.
If you want to go light on minions and have room left, add Savage Roar and Mark of the Wild to fill in the last spots, or if you want to be risky, go the Innervate/Wild Growth route. Moonfire though, is terrible unless all of your minions are spellpower based, which is a completely different setup.