In bronze? Play this champion. 
Start with
.
Laning phase: your plants are your largest source of spell damage, but don't forget autos. Zyra has a solid auto animation and can harass very hard when the enemy ADC goes for CS. If the enemy lane doesn't strike you as a threat (in champ select), even consider running hybrid penetration runes so your autos hit harder.
Once you hit level three, just wait for the enemy ADC to CS. E as he walks forward to root him, follow up with QW to spawn a plant on top of him. Procs Thunderlord's every time. Loads of damage. Once you start storing multiple seeds, you can even EQWW for yet more burst. Your goal is to zone the enemy ADC very, very hard. But remember that you're squishy. Don't get greedy.
First back, aim to buy either
or

if you're planning to farm a lot or the enemy jungler has a heavy gank presence. Otherwise, just build offensively, cover your flanks with a control ward, and buy your sightstone on second back.
Your core:
.
When ahead, build
before
. An early
does a ton of damage. Otherwise, just build
first.
Your boots (choose one):
.
is your default choice and usually what you buy if you can effectively gank mid. Helps you get deep wards in the enemy jungle which can thwart ganks. Super useful against aggressive early game junglers, like
.
if you need to secure your lane. I buy these when I need to hard carry my carry.
Finish your build with two of the following:

If you're carrying and the enemy team has a ton of CC and/or magic damage.
If the enemy team has a lot of dangerous AoE damage (e.g.
).
If the enemy team has a lot of CC, and you have a single fed carry that needs to be protected at all costs (e.g. a fed
).
If the enemy team has a ton of sustain (e.g.
).
Burst mitigation. Best when coupled with
.
Only as your final item, and only if you don't need anything else, build this to carry harder.
Cheap and adds tons of damage. You'll buy this in most of your games. The default choice.
If you're carrying and an enemy assassin (or two) is focusing you in team fights.
Sample final build:
.
Enjoy freelo.