An Augmented Triad is one that has the Major Third and a sharpened fifth.

As with triads that mess with the natural order of 'harmony' this triad produces a 'danger' or 'scary' type of sound. It has an intense flavor and would be used sparingly in the middle octaves. Another thing to understand is that this chord will not occur naturally in any key. The mysterious thing about this triad is that it will be replicated on guitar every four frets with a different enharmonic spelling with the same formation.

Augmented Triad: ROOT, M3, 5+

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The construction of the diminished chord is that we flatten the 3rd to create a minor triad then in addition we flatten the fifth creating the diminished triad.

Well, all bass players are going to come across a few these in their days and many won't even know what they are doing. A flat fifth is also know as something rather evil. Apparently it was a sin to play at some stage of our Christian history. Black Sabbath, although Christian, played the flattened 5th often. As it was a superstition that it would conjure the devil, sabbath would cloak their instruments, their clothing and their stage with crucifixes to ward off the evil. I'm not kidding about this.

Diminished Triad: ROOT, m3, ˚5

Having an understanding of Major Scale Theory and Major Triads will make this formation a simple execution. In fact, you would have probably come across this type of triad a long time before seeing it explained here.

Minor Triad: ROOT, m3, P5

So as for most chords we start with the root, then by playing the third of the major scale flat and the perfect 5th we have a minor triad.

As for any chord formation where the minor third shows in a pattern is irrelevant, as long as the bass or a chordal or melodic instrument does present it. If the minor third is not presented at any stage then there is nothing to indicate you have been on a minor triad. If you have played the the Major Third during the passage then you would have indicated it to be of the major variety.

Another way to look at this triad is too consider the minor scale being played from the root. You'll find that the third is the naturally occurring one in that scale.

You see, a minor scale is created by having a Flat 3rd, 6th and 7th. You can also create a minor scale by considering the relative Minor scale mode to the Major.

This is the most simple triad to create. It is a Major Chord. You can use this triad as the basis of creating other chords by altering it on the fly. As a bass player you can concentrate on these notes in a line using other notes in the Major scale as only passing notes. This is not a rule but the simple place to start exploring.

Major Triad: ROOT, M3, P5
This is the 1st, 3rd and 5th of the major scale. It is a simple as that.

For 6 string Guitar and Piano
On keyboard you may invert the chord to M3, P5, ROOT or P5,ROOT,M3 - these would be known as inversions. On guitar you may omit the 3rd in the first octave and play it in the second octave, it is also likely that you will repeat the ROOT and P5 an octave higher.

Things to know:
You will not always represent M3 in the first octave on a guitar or play simultaneous notes including the M3 in lower octaves on a bass. If a chord is being played by another instrument with only the ROOT and P5 the bass can introduce the M3 to emphasize that it is to be a Major - this applies in chord theory wherever a chordal sound is being produce with omitted intervals.