First of all, Pythagorean (PT), Just Intonation (JT) and Equal Temperament (ET) are different (families of) tunings. Therefore, note frequencies will be different in each case. You can find frequency charts for them on Wikipedia.
For any tuning, you need a reference frequency. Currently, 440 Hz for A above middle C is the most widely used standard. But historically it wasn't the case and some orchestras still tune differently.
PT is a family of tunings based on just perfect fifths, so it's a subset of the just intonation family. Perfect fifth is the transposition of the third harmonic of musical tones down to the same octave as the fundamental. Dividing a frequency by two transposes it down by one octave. Third harmonic's frequency is three times the fundamental. Therefore a perfect fifth is 3/2 the frequency of the fundamental.
PT works by starting on a selected frequency and moving in perfect fifths (and transposing them down to the same octave). So the frequency ratios are 1, 3/2, 9/8, 27/16... The general formula is
3^n/2^n (and then you transpose it back to your octave by dividing it by two as many times as necessary).
One problem is that a stack of perfect fifths can never add up to an octave. Circle of fifths cannot be closed. After 12 consecutive steps, starting from C, (C G D A E B F# C# G# D# A# E# B#) you end up with a B# that is close, but not quite equal to C; the ratio is
3^12/2^19 and it's about a quarter of a semitone sharper, which is very noticeable. In other words, C# ≠ Db in PT. As a result of this, if you want to live with only 12 notes, some of your fifths will be out of tune. It's called a wolf interval.
There is also another problem: The Pythagorean major third (81/64) is too sharp compared to the JT major third (5/4, see below). This renders this tuning mostly useless for triadic harmony.
JT is based on integer ratios. It strives to make all intervals just (if we only make the fifths just, it's usually labeled as PT). For example, a major scale can be created with the major triads (ratios = 4:5:6) built on the fundamental, perfect fourth (4:3) and perfect fifth. It will give you C=1 D=9/8 E=5/4 F=4/3 G=3/2 A=5/3 B=15/8.
This is harmonically very pleasing as long as you stick to the I, IV, V, iii and vi triads. But the ii triad is out of tune. These are the wolf intervals of this particular JT major scale. You can fix it by lowering the D for example, but this will break the G chord, and trying to fix it will break something else. It's impossible to get all the chords right without adding new notes to the scale.
What are the frequency ratios of the notes with accidentals then? The answer is, it depends. The minor seventh (Bb) can have the 16/9, 9/5 or 7/4 ratio depending on what effect you want to achieve.
Again, you will need more than 12 notes to use JT, even in a single key.
ET just divides the octave into 12 equal intervals. None of the intervals are "just" (save for the octave), but most of them are within almost tolerable limits: It's a compromise; there is no way of having the perfectly tuned just chords and freedom to modulate to any key you want with a reasonable amount of pitches (e.g. piano keys).
To hear the difference, listen to a good barbershop quartet and then play the same chords on an ET instrument like a piano. The nice, ringing qualities of the chords will be gone.
Anyway, ET divides the octave equally into 12, so the ratio between adjacent notes (like C and C#) is the twelfth root of 2 (
2^(1/12) ≈ 1.05946309436). You start from your reference frequency (say, A=440), and multiply it by this number for every consecutive note. Here's a chart.