What ways are available to give orders to animals summoned through the Summon Nature's Ally spells? I know that Speak With Animals is available, but especially in combat I may not have an additional spell slot + standard action to spare to get my creatures to do what I want. Can they be pushed?
Handle Animal could work, but it's a bad tactic. Summoned animals are still just animals, and all the tricks used to control normal animals work on them. If we assume that the animals would be receptive to your commands if they understand them, you should be able to Push them like any other animal.
But. Pushing takes a precious full-round action, because the summoned creatures aren't Animal Companions. This makes it more or less non-viable - even casting Speak with Animals as a standard action and then just telling the creatures what to do would be more action-efficient.
Fortunately, even if you don't give them the order to attack a particular enemy, remember that
Summoned animals attack on their own. From Summon Nature's Ally I:
So at the very least, the animals know who your enemies are, and will do their best to harm them. They might not make super-strategic decisions on their own, but they won't sit around like golems waiting for instructions.
If you find yourself in a situation where you need fine-grained control over a creature, you can...
Summon smarter creatures. When you really need a monster to do something far more specific than "maul the bad guy's face", the Summon Nature's Ally list has lots of smart critters that speak real languages. Fortunately, the creatures that are capable of performing the most delicate tasks (Unicorns that heal, Xorns that scout, and so on) tend to fall into that group.
If you regularly want a particular, dumb, animal to precisely understand your orders, you can...
Invest in a Torc of Animal Speech from Masters of the Wild (admittedly a 3.0 book). Costs 12,000 gp, allows the wearer to use Speak with Animals at will. Not quite continuous, but refreshing it once every 5 or so minutes would make sure it's up in every combat. I find it expensive for what it does, but there it is.
I find it especially expensive considering that...
This is frequently handwaved away. Managing summoned monsters is a lot of work to begin with. Most groups I've played with simply don't bother with the additional work of managing communications. You may want to ask yourself and your group what you are gaining from it.