Quoting the suggestions written by a TA forum poster :

(1) Go to http://www.machupicchu.gob.pe. Clicking on the UK flag translates some, but not all of the text to English. Under “Compra En Linea” on the left, you can choose MP and the HP reservation times for the date you want to go. You can see the number of spots left near the top. It lets you enter how many adults in your party at this point. This is all Step 1.

(2) Click on Step 2. Put in the names, country, age, gender, and passport numbers for everyone in your party. U.S. is of course Estados Unidos.

(3) Click on Step 3. From the text below, it looks like your e-mail address should go in the Address box. Check the box to accept the conditions the click on RESERVE GENERATING. A reservation form document will open. Make note of the reservation number. DO NOT TRY TO PRINT TO PDF. This is where the browser crashed…twice. Acrobat and Flash did not play nice and had to start over. You’ll have a chance to print later on. Again, don't forget to write down the reservation number.

 

At the present time (May 2013) the CREDIT CARD SYSTEM is UP.  However you must switch to the Spanish language verion of the website before attempting "PAGOS". Click the Yellow and Red flag. You can use Google Translate or look at the English version of the website if you cannot understand Spanish, but do not try to make your payments other than under the Spanish version.

(4) Close the windows and click on the PAGOS tab near the top of the page (Pagos=  payments in Spanish). The fine print in the reservation form says that the reservation expires in 6 hours if it’s not paid in person or on the Internet. Make sure pop-ups are allowed in your browser. Enter your reservation number and click on Pay. The new window will let you put in your credit card information. They require a Verified by Visa card. (You can activate your Visa at https://usa.visa.com/personal/securit...

 

(5) Once you’ve paid, you can go back to the main page and click on the CHECK-IN tab. When you put your reservation code in again and search for it, you can click on IMPRIMIR TICKET to print your tickets. If your payment hasn’t been processed, you will just get the reservation form again, but this time it will say that it’s paid (“pagado”) in the upper right corner. After a while when you go back and try this step again, you will see the actual tickets. You can save this as a PDF or print.  This could take a while.

The automatic cancellation of reservations without payment after 6 hours, and requirement of government-issued identification should help ensure travel agents do not hoard tickets. In the future, it might be that getting to climb HP will be nearly impossible if you haven’t planned long ahead of time.