How can I type left (sub)superscript?

Rather using manual typesetting tricks, I suggest you define template boxes for these three notations. Add the three styles below to your document's style definitions. (In case you're not familiar with the style editor, to do this: Format > Edit Stylesheet...; and for each of the 3 styles, start typing to create a new cell, press Ctrl-Shift-E to edit the code, and replace with each cell code shown below, and press Ctrl-Shift-E.)

LeftSuperscript style:

Cell[StyleData["LeftSuperscript"],
 TemplateBoxOptions->{
  DisplayFunction->(RowBox[{
   SuperscriptBox[" ", #2],
   "\[NegativeVeryThinSpace]",
   #1
  }]&),
  Tooltip->Automatic}]

LeftSubscript style:

Cell[StyleData["LeftSubscript"],
 TemplateBoxOptions->{
  DisplayFunction->(RowBox[{
   SubscriptBox["\[InvisibleSpace]", #2],
   "\[NegativeVeryThinSpace]",
   #1
  }]&),
  Tooltip->Automatic}]

LeftSubsuperscript style:

Cell[StyleData["LeftSubsuperscript"],
 TemplateBoxOptions->{
  DisplayFunction->(RowBox[{
   SubsuperscriptBox["\[InvisibleSpace]", #2, #3],
   "\[NegativeVeryThinSpace]",
   #1
  }]&),
  Tooltip->Automatic}]

Input

The boxes themselves are written using box expressions like TemplateBox[{"x","y"}, "LeftSuperscript"].

For convenient editing, also create input aliases, by adding another cell to the stylesheet:

Cell[StyleData[All],
  InputAliases->{
    "l^"->TemplateBox[{"\[SelectionPlaceholder]","\[Placeholder]"},
    "LeftSuperscript"],
    "l_"->TemplateBox[{"\[SelectionPlaceholder]","\[Placeholder]"},
    "LeftSubscript"],
    "l_^"->TemplateBox[{"\[SelectionPlaceholder]","\[Placeholder]","\[Placeholder]"},
    "LeftSuperscript"]
}]

Then, you can create left superscripts (Esc l ^ Esc), subscripts (Esc l _ Esc), and subsuperscripts (Esc l _ ^ Esc) while editing using the respective input shortcuts.

Output

To get Mathematica to display the typeset forms in the output, execute

LeftSuperscript /: MakeBoxes[LeftSuperscript[braw_, supraw_], form_] :=
  With[{
      b = MakeBoxes[braw, form],
      sup = MakeBoxes[supraw, form]
    },
    TemplateBox[{b, sup}, "LeftSuperscript"]
  ];
LeftSubscript /: MakeBoxes[LeftSubscript[braw_, subraw_], form_] := 
  With[{
      b = MakeBoxes[braw, form],
      sub = MakeBoxes[subraw, form]
    },
    TemplateBox[{b, sub}, "LeftSubscript"]
  ];
LeftSubsuperscript /: 
  MakeBoxes[LeftSubsuperscript[braw_, subraw_, supraw_], form_] := 
  With[{
      b = MakeBoxes[braw, form],
      sub = MakeBoxes[subraw, form],
      sup = MakeBoxes[supraw, form]
    },
    TemplateBox[{b, sub, sup}, "LeftSubsuperscript"]
  ];

Result

It looks reasonable in both code and typeset-math forms, except for the LeftSubsuperscript when the subscript and superscript differ greatly in length:

Discussion

Template boxes are harder to mess up while editing than manual typesetting.

Another advantage of using semantically-correct typesetting is that the boxes can be parsed and manipulated as expressions. For example, if you want to use $^y x$ to denote tetration—

Tetration[a_, n_Integer] := 
    If[n == 0, 1, a^Tetration[a, n - 1]] /; a > 0 \[And] n >= 0;

— you could define

LeftSuperscript = Tetration;

and use it:

resulting in:

You could also symbolically manipulate or generate expressions containing your notation.

I don't know how you would type this in directly, but the following may get you a step closer.

How about leaving a placeholder?

Row[{Style[Subsuperscript[Invisible["x"], "a", "d"], Italic], 
     Style[Superscript["F", "'"], Italic]}]//TraditionalForm

There is quite a bit of "micro" tweeking available for typesetting these positions. Starting with Davids answer:

Row[{
   Style[Subsuperscript[Invisible["x"], "a", "b"], Italic], 
   Style[Superscript["F", "\[Prime]"], Italic]}] // TraditionalForm

you can use "\[InvisiblePrefixScriptBase]" instead of Invisible["x"] as per @kgulers answer here. The advantage in doing so is that you do not have unwanted space to the left of your typeset expression. Then adjust the vertical positions of your sub and superscripts:

Row[{
   Style[Subsuperscript["\[InvisiblePrefixScriptBase]", "a", "b"], Italic, 
    ScriptBaselineShifts -> {0.65, 0.75}], 
   Style[Superscript["F", "\[Prime]"], Italic, 
    ScriptBaselineShifts -> {Automatic, 0.85}]}] // TraditionalForm

And you can also nudge subscripts and superscripts in inline cells around via the Insert>Typesetting menu or programmatically with AdjustmentBox. Here I am moving a and b to the right, closer to F.

Row[{
    Style[
     Subsuperscript["\[InvisiblePrefixScriptBase]", 
      AdjustmentBox["a", BoxMargins -> {{0.17, -0.17}, {0., 0.}}], 
      AdjustmentBox["b", BoxMargins -> {{0.17, -0.17}, {0., 0.}}]], 
     Italic, ScriptBaselineShifts -> {0.65, 0.75}], 
    Style[Superscript["F", "\[Prime]"], Italic, 
     ScriptBaselineShifts -> {Automatic, 0.85}]}] // 
  DisplayForm // TraditionalForm

Finally you can control the size of the subscripts and superscripts with ScriptSizeMultipliers

Style[
   Row[{
     Style[
      Subsuperscript["\[InvisiblePrefixScriptBase]", 
       AdjustmentBox["a", BoxMargins -> {{0.17, -0.17}, {0.5, 0.}}], 
       AdjustmentBox["b", BoxMargins -> {{0.17, -0.17}, {0., 0.}}]], 
      Italic, ScriptBaselineShifts -> {0.5, 0.75}], 
     Style[Superscript["F", "\[Prime]"], Italic, 
      ScriptBaselineShifts -> {Automatic, 0.85}]}], 
   ScriptSizeMultipliers -> {0.6}, ScriptMinSize -> 6] // 
  DisplayForm // TraditionalForm