In TAB notation, whenever there are legato sections of tied notes, you should pick / strum the first note of the set and then use hammer-ons and/or pull-offs to sound the other notes. In your first example, if you follow the notation exactly, you should fret the note on the eighth fret on the low E string (using your middle finger), pick it, then hammer-on to the tenth fret (using your fourth finger for this) and then pull-off back to the eighth (your second finger should remain on the eighth fret throughout). Then, do the same starting on the seventh fret, hammering-on to the eighth and then pulling-off back to the seventh.
In the second example, you should continuously hammer-on and pull-off on the second and third frets. When doing these longer runs, your "pull-off" needs to slightly "twang" the string in order to sustain the note long enough for it not to die out before the end of the legato section.