There are a bunch of strategies, but since any way to get obsidian requires lava, first and foremost you're going to have to be careful.
Always carry around a bucket of water with you. Remember that you can place the water on the ground, wait for it to spread, and then collect the source block back up. Use this to turn lava into obsidian before getting to near it. You are much better off turning lava into obsidian and mining it in place than trying to move the lava somewhere else and changing it into obsidian there.
Remember that lava produces light, so while it may protect you from spawning mobs, when it changes to obsidian it won't. Light the area with torches before changing the lava to obsidian.
If you're feeling really brave, you can always make a portal to the nether and collect lava there to bring back with you, if you run out of lava in the real world.
Sometimes the lava is really hard to get to safely. If you don't feel comfortable trying to maneuver your way around, it is perfectly fine to abandon that lava spring in favor of a more accessible one. It is always easier to find lava in a cave system than try to mine it out of a pocket surrounded by stone. Just make sure you mark lava somehow (signs work well) so that you don't accidentally dig there in the future and get yourself killed.
When a lava spring is multiple blocks deep, it can be hard to mine the obsidian because the block may fall into the lava directly below it. Make sure you never mine directly below yourself, and don't go diving after the obsidian hoping to catch it before it falls into the lava. These can be especially tricky to mine. Change additional lava to obsidian as it is revealed to minimize risk.
Most importantly, just remember the main mantra: be careful.