Q:

How can ordinary plants be turned into creatures?

I'm a GM, and I'm comfortable exercising Rule 0 where appropriate, but I prefer to play by the rules if/where possible. 
What I want to do
I want to take an ordinary plant, [do something], and have it be a creature—preferably permanently:

So that it has ability scores
So that it can be targeted by certain spells
So that it can wear magical items (or even have "item slots")

Possible uses:

It could be trained like many other animals (via Handle Animal)
It could be an animal companion or familiar
It could be a minion via the Leadership feat
It could inspire a fun NPC or villain: a druid who has a bunch of plants following them 
If a party found exotic plants with interesting uses (if the plant were sentient), they could take the plants with them. (Examples: a sentient tuber guarding something could burrow itself into the ground if it detected an intruder and trigger a trap or ward on behalf of its master. A sentient poisonous vine could be taught to distinguish between friends and foes.) 
An animated tomato plant could effectively counter a bardic performance-based skill/action by hurling rotten tomatoes at the performer. ;-)
Easter eggs for a casual session (example)

Similar stuff (and why it's insufficient)
It seems there are hints of a plant-mastering druid, but it never really evolved into an archetype. 
The Animate Plants spell is great, but:

It's a 7th-level druid spell (available at Druid level 13), which seems overkill for animating tiny plants, such as a carrot. 
It lasts either tens of rounds. It isn't permanent and isn't on the list of spells that can be made permanent — though, one could easily say that since Animate Object is on that list, Animate Plants ought to have been on the list, since it's the same in spirit. 
It doesn't grant ability scores. 
It doesn't offer independence of thought, emotion, will, etc. Animated objects (and animated plants by extension) attack whatever the caster initially designates. 

The Grow Plant Creature feat is awesome because it explicitly allows for druids to create sentient plant companions, but:

It has a very limited selection of creatures, and no rules for extending this to plants not on this list. 
Such plant creatures must be grown — they cannot be made out of an existing plant. 

The Awaken spell is almost perfect, except:

The only plants that it affects are trees—not all mundane plants (of course, this could be modified).
It brings trees or animals to human-like sentience (high ability scores). This seems overkill. 

See also

Can I have plant allies?
Do all plants count as "creatures"?

A:

Use the Treesinger druid archetype.
In the Advanced Race Guide there's a racial archetype for elves that lets a druid do exactly this. It introduces four plant-companion options: 

Carnivorous Flower
Crawling Vine
Puffball
Sapling Treant

If you're looking for a creature the party can come across in the wild, you could just use the stats for these companions (possibly increasing their effective druid level based on the party's APL).

A:

http://www.d20pfsrd.com/magic/all-spells/a/awaken/
Start with the Awaken spell as a base, and do magical research to modify it to work on any plant, instead of just trees.
If you ask your DM nicely, they might be fine with "accidentally" misreading "any tree" as simply "any plant" without even any real research needed on your characters' part. (I can't see why it doesn't apply to all plants to begin with. It even describes it as "an awakened plant" within the spell.)
Sadly, with this spell existing, I don't think you'll find anything closer to what you want pre-existing in the game.

