Moving Silently can be attempted each time the thief moves.

It can be
used to approach an area where some creature is expected, thus
increasing chances for surprise (q.v.). or to approach to back stab, or
simply done to pass some guard or watchman.
Failure (a dice score in excess of the adiusted base chance) means that movement was not silent
(see SURPRISE). Success means movement was silent. (SILENT MOVEMENT)

DMG:

Moving Silently: Silent movement is the same as normal exploratory movement,
    i.e. 12' per round as the thief creeps up (croodles) upon the AREA or victim or whatever.
Do NOT inform the thief that his or her dice score indicated a lack of success at this attempted stealth,
    if that is the case.
He or she thinks the movement is silent,
    and the monster or other victim will inform the character of his or her misapprehension soon enough.

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LTH: The Thief (d47, bd5)
Moving silently is only abused when
the DM forgets that the rate of movement
is only 12 feet a round (DMG, page
19). If the thief moves faster, reduce the
chance of silence by as much as 3% per
foot of movement above 12 per
round. The actual surface being crossed
wilt dictate the proper subtraction (ranging from ½% to 3% per foot). It should
also be noted that the thief using a SiIence 15’ Radius spell will have that
sphere of silence hit his/her victim while
the thief is stilt 15 feet away; a sudden
lapse into silence will often alert a victim.

Circumstances must be considered in
such a case. It should also be remembered that Boots of Elvenkind do assume
some slow rate of movement — not
12 feet a round, but not running either — in order to function properly. A
speed of up to 1/2 of the thief’s normal
walking speed would allow the boots to
function as designed. A higher SPEED
would begin to negate their effectiveness.

Quote:
How did you handle situations where a character of one class (say Fighter) was attempting to use Move Silently or Climb Walls - Two situations that when taken literally (i.e. - the Thief can Move with ABSOLUTE SILENCE whereas someone else might attempt to move stealthily, and the Thief can climb SHEER SURFACES wheras someone else might climb a rough cliff, or a tree), would mean that only the Thief could attempt them, but when looked at in a broader fashion, might be allowed for a character of any class ?
 

Generally common sense was applied.
A fighter in metal armor can't move silently, but without that impediment a Dex ability roll with modifiers for surface and/or footwear, would be called for.