Op Amps - please help me know how to use them

I really need help learning to use op-amps. I am a knowledgeable individual in regards to Arduino and basic circuits, but I still struggle in some of the more advanced electrical engineering things, such as op amps. Adafruit sells an op-amp here (http://www.adafruit.com/products/808), that they have a nice tutorial for, and that I am definitely going to buy. However, I want to become capable of using non-rail to rail op amps too, so I thought I’d grab some from other sources to play with too, for my learning.

Why do I need an op amp?
-My goal is to measure current, using very low resistance resistors from DigiKey. ex: 0.001 Ohm to 0.01 Ohm.
I want to have several different setups, that range from 10A DC to 100A DC, as well as wall current up to 1A AC and 10A AC.
-that’s where the op amp comes in—to amplify the voltage drop across the resistor so that it has a range of 0-5V for the ADC on the arduino.

I am looking at the following online, and have downloaded the datasheets for many of them (see attached files):
TL072 - http://www.ti.com/lit/ds/symlink/tl072.pdf
NE5532 - http://www.taydaelectronics.com/datasheets/A-031.pdf

What parameters should I look for? How do I hook one up? (can they all be used as this shows? - http://www.adafruit.com/blog/2011/11/02/almost-all-opamp-circuits-you-will-ever-need-with-formulas/)

Additionally, some (such as the NE5532, datasheet link above) specify the input should be +/-5V to +/- 15V (operating conditions), and some only specify Absolute Maximums. Does the Arduino (0V ground and +5V Vcc) meet this condition, or would it have to be -5 to +5 to meet the operating condition of +/-5V minimum?

How do I know what the max gain is that I can use, or what max resistors I should use?

Are these biased? What is a bias and how to I account for it? It seems they are not rail to rail, but I’m not sure what that means.

Thanks for any help you can give!

TL071 datasheet.pdf (281 KB)

TL072 datasheet.pdf (1.7 MB)

TL084 datasheet.pdf (312 KB)

TS922 Rail-to-rail high output current dual operational amplifier datasheet.pdf (542 KB)

I think you have a good start already understanding op-amps.
Here is a good reference:

That link from TI is "Op Amps for Everyone", and is the link I'd have given. Very good resource.

I downloaded the PDF. It is over 400 pages. It'll take me many many hours to figure out how to use an op amp I suppose, but I'll make my way through it as necessary. Thanks for the link.

I am glad you didn't expect one of us to type out 400 pages for you.

I am glad you didn’t expect one of us to type out 400 pages for you.

Of course not :), but a 1-page summary of how to solve my particular problem is always welcome.

For instance, if someone asked how a transistor works because they wanted to use PWM on a motor, or power a relay, I’d explain that a BJT NPN transistor would work well for this, and I’d write them this post, show them this diagram, and give them my excel spreadsheet detailing my work and equations (it’s downloadable at the bottom of my post here):

I’d also explain that the parameters that should matter most to them are hFE (gain) and IC (collector current), and that so long as IC is high enough to power their motor and so long as the current they need / the lowest hFE given in the datasheet <= ~30mA, their Arduino can use it.

I’d also give them this link where they can get 10 good NPN transistors for $1. http://www.ebay.com/sch/i.html?_odkw=pn2222&LH_BIN=1&_sop=15&_osacat=0&_from=R40&_trksid=p2045573.m570.l1313.TR0.TRC0.Xpn2222+npn&_nkw=pn2222+npn&_sacat=0

**Op Amps have so many functions, uses, and nuances its quite overwhelming, and I don’t know what a standard op-amp is, or how to tell if it even meets my specs. And all I want to do is amplify a signal from 0.1V to 5V. **
**I do appreciate the link, and over time I’ll come to understand a great deal of it, but if anyone can say, “buy this one because I know it works,” that’s good enough for me to buy it and figure it out more when it comes. **
Again though, I do appreciate the responses given thus far.