So Brand has high base damage, this means that you outscale him. You need to let the enemy laners push to you and just cs as best you can and wait for your jungler to come and gank that juicy 300g Brand
In lane Brand just wants to throw his W's at you when you go to cs. So you just lose a few cs, this way he cannot get his frostfang gold. If brand gets no kills and not enough ff gold, at a certain point in the game he becomes useless
Zyra isn't really a poke champion. She needs to hit her E to land any kind of combo, so in lane all she does is fish for E's. If she lands one she just WWQ on you and you take lots of damage, get ignited and you probably die. So with this knowledge you need to anticipate zyras roots and try to dodge them. If she doesn't land the root, after a certain point, you just jump on her and 3 shot her because she has nothing else but her ult to stop you. Her plants can be a pain but if you coordinate with your support to hit them, they die after 1 tick of damage
Bush wards are really important vs both, but especially zyra. Also frostfang gives them 20 on-hit damage so their autos hurt and give them 20 gold. Just be sure to really punish their cooldowns, as they are no threat when Zyra's E or Brand's W is on cooldown.
Often you might take a Brand W and back off as an ashe, but a pro player might decide to trade back damage immediately, flash over his Q and kill him
But ye, just remember to punish cooldowns at least