Every form of life is made of two parts, one physical and one ethereal. The ethereal, the "soul" if you wish, is what allows an otherwise physical being such as an elven to manipulate the ethereal force known as magic. Even then, rarely is an elven alive who can manipulate magic that is not itself part physical, even if that physicality is just lightwaves. Magic that works with existing forms works by interacting with the ethereal parts of those forms. The ethereal is connected to the mind, in varying degrees. A life form that does not otherwise have a mind, can be magically induced to thoughts by affecting their ethereal selves.
Veldt elven magic works on these principles. Elven can communicate with other beings, even animals, using veldt elven magic. While baboons, for example, cannot communicate with each other (lacking the concept of "other"), veldt elven can communicate with them using magic. They may not associate the communication with the elven speaking to them, but this barrier can be worked around.
The same principles work with plants. Plants, not normally being considered thinking forms of life, can be made to think at near-elven levels with enough magic. The most obvious example of this is the dryad, in which strong forest elven magic can create elven women out of trees, that can think for themselves (though generally dryads created in this matter are not considered to reason).
Every living thing has certain sensibilities. Even if these are not thoughts, are not signals in a brain, they exist at some level. For example, plants undergo chemical reactions that cause them to follow the sun. This cannot be considered a rational choice, it's just something that happens chemically, automatically. Animals have certain instincts, and live certain lives. For example, some animals have a stronger maternal instinct than others. These predilections and instincts will manifest as thoughts if the life forms are prodded towards awareness. Intelligent plants will like the sun.
The ethereal side, the souls, of life forms will remember things even if the life forms cannot. Thus, if a tree has been made a dryad before, the next time it is made a dryad, it will be able to tell you about its previous time so enchanted. It will remember any skills it was taught the time before, and remember people it met. Life forms will also remember things that happened when they were unenchanted, but only in vague terms. Most especially beings without eyes will not remember seeing something, except from any time they were enchanted with eyes. A wolf will not remember what someone said, if they spoke near it without using magic, but it will remember that someone was near it and that the person spoke.
Each living thing has some sort of personality. That personality will either be the same as the animal itself, or be something that is a logical extension of the type of life the being has lived, and its natural tendencies. In a pack of wolves, for example, each animal will have its own role and own personality. When speaking to one of them magically, that personality will come across. This will be most notable if you are trying to get something from the wolf, from the answer to a question, to assistance with an enemy. You must also consider its current loyalties. Animals can lie, and some are known for their tricks, they will be just as tricky enchanted as otherwise. Obviously certain spells can compell others to behave certain ways, but most of these are reserved for elven.
Plant personalities are a little harder to guess. Some might be generous, some might be spiteful, even if both are apple trees. To some extent it depends on their past experiences with elven, but even if they've never been enchanted before, they might have different responses due to different events in their lives. Maybe one of them weathered a storm better than the other did. It's impossible to be certain what a plant's personality will be like before you talk to it, but you can try to guess based on their outward appearance: if they look healthy, clean, unscarred by time and fruitful, they will most likely be friendly. In general plants will sense a kindred spirit, as will animals, so someone who has spent a lot of time communing with nature nonmagically or who gives beneficial spells freely will likely be well received.