I know this answer seems long. I encourage people to read it entirely: I figure most people who do so will learn about some commonly supported behaviors.
The fast answer to your question is: it depends. Your best bet is to try pressing Alt, and then tapping the letter twice. However, that isn't entirely consistent.
If you press Alt and hold u, it rapidly cycles between the two.
My guess is that you'll get the same result if you just hold Alt and press the U key multiple times. When holding down Alt-U, the program may be interpreting that as if you just pressed U multiple times (similar to what a text entry field, such as a Notepad window, will do when you hold down a letter key when you're not using a menu). You may also get the same result by just pressing Alt (and then releasing Alt) and then pressing the U key multiple times.
Now that I've tried to provide direct answers quickly, here is my lengthier explanation of the behavior, starting with a counter to a statement made in the original question:
Most anyone who's used a computer for more than a month knows
Nope. I find this unfortunate, but many people have not figured that out. This is probably becoming more true over time since newer versions of Microsoft Windows tend to hide the underline in many pieces of software, by default. (Although, there is an Accessibility option to re-enable the underlines in many programs. For instance, in Windows 10: Control Panel, "Ease of Access center", "Make the keyboard easier to use", and then in the "Make the keyboard easier to use" section, "Underline keyboard shortcuts and access keys".)
Because the option of pressing Alt is becoming less-known, newer software may be less likely to bother implementing such keys. Here's another example of keys that may be less commonly known: With the IBM Common User Access ("CUA") standard, you can press Shift-Delete to cut, and Shift-Insert to Paste. (And Ctrl-Insert to Copy, but who needs to copy text when you can just Cut and then Paste real quick?) Microsoft Windows has supported that for a long time. However, Microsoft has been more prone to document Ctrl-X for cut, Ctrl-C for copy, and nearby (on US QWERTY, anyway) Ctrl-V for paste. The result is that more people are familiar with the later shortcuts.
Maybe you knew about those. Did you know that CUA also specified that you can press F10 to call up the menu, similar to the more-well-known Alt key? When you've tried that in various programs and found that works too, then the choice for "Shift-F10 for context menu" (similar to right-clicking) seems like a rather logical choice (and therefore, in my opinion, a rather sensible choice) that Microsoft made, rather than the choice of Shift-F10 just being a totally random decision that they came up with (when they started encouraging "right-click menus" with the release of Windows 95).
The reason I mention the CUA shortcuts is just to demonstrate a point that is rather important to this answer: Many people don't know about some of the behaviors that are (at least somewhat) widely supported (and, therefore, at least somewhat widely expected or at least appreciated when they are supported.) This is true even though some of these behaviors are part of an old official standard that has been with us for a very long time. The effect of some standard behaviors being lesser-known is that these behaviors seem to be supported less-widely, by a wide variety of programs (especially smaller third party programs).
Likewise, the behavior that is being asked about (when there are multiple menu options with the same letter) is a behavior that I've seen vary. Sometimes this is just caused by a program where the program designers weren't careful to prevent it, and there is no way to select the option by using the underlined letter. Call it a bug, if you like.
However, if the multi-underlined letter is usable somewhat sensibly, this is how I've seen it work:
If you press Alt, you make the menu system active. Then, if you press a letter that corresponds to exactly one menu option, then that option is chosen. (I'm making up this word chosen, and refer to the behavior that happens as if you clicked on it with a mouse). If you press a letter that corresponds to more than one menu option, then the "first" menu option that uses that letter will be selected. (Again, I'm just choosing a term I came up with. By "selected", I do mean something different than what I meant when I said "chosen".)
For a button, the effect of selecting it may involve a dotted box appearing over a button, similar to getting it selected with the Tab key. For a menu option, the effect of selecting it may involve highlighting the menu option, similar to if you managed to get the option highlighted by using arrow keys.
If you press the same letter again, the currently selected option will un-select(/de-select), and another available option will be selected. Once you have the desired option selected, you can press Enter to actually choose the option, similar to if a mouse cursor clicked on the option.
Note that the order that the access keys get cycled through can be inconsistent. When I mentioned the "first" option (earlier in my text), that refers to the order in which the program keeps track of the available shortcut keys, which usually involves the upper-most or left-most option being first. However, when programmers create programs that use this less-intuitive approach, they might also have been a bit sloppy when it comes to the order in which these options appear, so prepare for the possibly-unexpected.
That is the most common behavior that I remember experiencing, in the admittedly-unusual case of running across this scenario. In most cases, programmers who support underlined letters have taken the care to avoid such re-use (by choosing non-conflicting letters).
A notable exception is that I've noticed Microsoft Outlook 2016 can have a letter repeated. In that case, the access keys are not shown as underlined letters, but little boxes, and the little box for the repeated letter will actually have two keys for you to press, e.g. Y1 and Y2. (That might only happen if add-ons are added?)