How to play a quicker game of Monopoly?
First of all make sure you are following the base rules for Monopoly as there are a lot of different house rules that are used that make the game take much longer then it should. Judging on the accepted answer it seems that you are indeed using some house rules that make the game take longer.

I am including 3 rules that are commonly changed by house rules that make the game take much longer, though there are other house rules that cause problems.

Also I have included some official suggestions on making a game shorter.

Official Rules

Buying Property.

When someone lands on any unowned piece of property it will either get purchased by them or by someone at auction so there should be no reason to need more money to buy property at the start.


  BUYING PROPERTY… Whenever you land on an unowned property
  you may buy that property from the Bank at its printed price. You
  receive the Title Deed card showing ownership; place it face up in
  front of you.
  If you do not wish to buy the property, the Banker sells it at auction
  to the highest bidder. The buyer pays the Bank the amount of the bid
  in cash and receives the Title Deed card for that property. Any player,
  including the one who declined the option to buy it at the printed
  price, may bid. Bidding may start at any price.


Free Parking

This space does not give the player that lands there anything.


  “FREE PARKING”… A player landing on this place does not receive
  any money, property or reward of any kind. This is just a “free”
  resting place.


Passing Go

You do not get double the amount for landing on go


  “GO”… Each time a player’s token lands on or passes over GO,
  whether by throwing the dice or drawing a card, the Banker pays
  him/her a $200 salary.
  The $200 is paid only once each time around the board. However, if
  a player passing GO on the throw of the dice lands 2 spaces beyond it
  on Community Chest, or 7 spaces beyond it on Chance, and draws the
  “Advance to GO” card, he/she collects $200 for passing GO the first
  time and another $200 for reaching it the second time by instructions
  on the card


Suggestions from the rules for a short game

Suggestion 1


  There are five changed rules for this first Short Game.
  1. During PREPARATION, the Banker shuffles then deals three Title
  Deed cards to each player. These are free— no payment to the Bank
  is required.
  2. You need only three houses (instead of four) on each lot of a
  complete color-group before you may buy a hotel. Hotel rent remains
  the same. The turn-in value is still one-half the purchase price, which
  in this game is one house less than in the regular game.
  3. If you land in Jail you must exit on your next turn by 1) using a
  “Get Out of Jail Free” card if you have (or can buy) one; or 2) rolling
  doubles; or 3) paying $50. Unlike the standard rules, you may try to
  roll doubles and, failing to do so, pay the $50 on the same turn.
  4. The penalty for landing on “Income Tax” is a flat $200.
  5. END OF GAME: The game ends when one player goes bankrupt.
  The remaining players value their property: (1) cash on hand; (2) lots,
  utilities and railroads owned, at the price printed on the board; (3) any
  mortgaged property owned, at one-half the price printed on the board;
  (4) houses, valued at purchase price; (5) hotels, valued at purchase
  price including the value of the three houses turned in.
  The richest player wins!      


Suggestion 2


  TIME LIMIT GAME… Before starting, agree upon a definite hour of
  termination, when the richest player will be declared the winner.
  Before starting, the Banker shuffles and cuts the Title Deed cards and
  deals two to each player. Players immediately pay the Bank the price
  of the properties dealt to them