Is there any particular configuration required to connect to a mining pool with more than one client using the same wallet?
Do I simply start the same command line on each machine?
Nothing special to do if you're pool mining. Most pools just use your address as your "account name" and don't care if one device or 100 are mining to that address. As an example, some miners periodically point their miner to the Dev's donation address as a way to contribute.
A small caveat... it could be best to pick one pool and devote all your resources to that pool. The reason being that you build up your mining shares quicker and thus get your payout quicker (most pools have a 0.3 to 1.0 XMR minimum payout which could take a few days for small miners to achieve). On the flip side, you can probably even out your luck by mining to multiple pools... if one gets lucky and the other unlucky, you will get paid more in proportion to what you probably expected.
You can start the same command line one each machine and it will work. However, if you have hardwares with significant difference in hashrate, it may be better to target a specific difficulty. That can be done by choosing the pool port and/or, if the pool handles it, by specifying a worker id.
From dwarfpool http://dwarfpool.com/xmr :
You can determine your rigs separately for better vardiff, lower rejects and detailed statistic. Use username with any number (integer, any random number): WALLET . WORKER-ID