How to assign value to bidirectional port in verilog?

If you must use any port as inout, Here are few things to remember:

1. You can't read and write inout port simultaneously, hence kept highZ for reading.
2. inout port can NEVER be of type reg.
3. There should be a condition at which it should be written. (data in mem should be written when Write = 1 and should be able to read when Write = 0).

For e.g. I'll write your code in following way.

module test (value, var);
  inout value;
  output reg var;

  assign value = (condition) ? <some value / expression> : 'bz;

  always @(<event>)
    var = value;

endmodule

BTW When var is of type wire, you can read it in following fashion:

assign var = (different condition than writing) ? value : [something else];

Hence as you can see there is no restriction how to read it but inout port MUST be written the way shown above.

I hope that explains it to you.