I'm trying to pick an op-amp and I'm having trouble figuring out if the op-amp needs a positive and a negative power supply or if I can connect it to ground and the positive supply.
What do I need to look for in the datasheet?
Also, where do I find the "drop-out" of the output compared to the rail voltage?
Most if not all op-amps can be used in either configuration. Voltage is relative, and "ground" is just an arbitrary potential that you assign the value of 0 volts. There are op-amps "optimized" for one configuration or the other, but they can be used in either. This op-amp, for instance, is "optimized for single supply operation", and they emphasize features like:
but "Specifications at ±15V are also provided."
Op-amps meant for single-supply often have rail-to-rail outputs, which will usually be featured on the front page of the datasheet. To find the "drop-out", look for a graph like "Maximum Output Voltage Swing vs Load Resistance" in this datasheet.
All op amps have two power pins. In most cases, they are labeled VCC+ and VCC-, but sometimes they are labeled VCC and GND. This is an attempt on the part of the data sheet author to categorize the part as a split-supply or single-supply part. However, it does not mean that the op amp has to be operated that way— it may or may not be able to operate from different voltage rails. Consult the data sheet for the op amp, especially the absolute maximum ratings and voltage-swing specifications, before operating at anything other than the recommended power-supply voltage(s).
depending on the design of the op amp the drop out of the op amp won't be constant.
For example just because the drop is 1.5V with +/- 15V supplies doesn't mean it will be 1.5V with 0/5V supplies.
The LF347 you mentioned for instance does not have a constant drop out across input voltage options. Theres a graph in the datasheet showing this.
The actual output swing will vary with a few things:
You have to consider all these in determining your maximum output swing and these numbers are usually defined in the graphs in the datasheet.
When you look for an op amp for a specific purpose you can get away with generic op amps but you will find better performance in parts designed for the task at hand. The op amp designers usually attempt to mitigate some the variations i've listed above for particular applications.
For instance usually rail to rail op amps can drive the output to the rails when the output is open circuit but you will still find they will not drive all the way to the rails when driving a real load and could be substantially under the rails if a large amount of current relative to their rating is sourced/sunk. Additionally rail to rail op amps usually have low drive capabilities.
First, what you call "drop-out" can be found on page 3 of the datasheet as output voltage swing. At \$\pm\$ 15V power supply the output voltage swing for the LF347 is minimum \$\pm\$ 12V.
Voltage is not absolute, but rather relative to some reference point. If \$V_+\$ is 30V higher than \$V_-\$ for the opamp this might be a dual, \$\pm\$ 15V supply as well as a single +30V supply. It works exactly the same. It's you who decides where the reference, ground, lies.
Single supply opamps are often used with low supply voltages, like +5V. You'll have to keep output voltage swing in mind; if the output doesn't come closer than 2V from the rails a 5V opamp's output will be limited to +2V to +3V. Therefore low-voltage opamps are often RRIO, for Rail-to-Rail I/O. Outputs will go to a few tens of mV from the rails, and input signals close to the rails will be handled correctly as well. Non-RRIO will accept any input voltage as long as it's between the rails, but voltages close to the rails won't be amplified correctly.
