Is it safe to travel by Trains in India
Travelling by train in india is safe but make sure you travel by AC class and avoid Non AC travelling and just make sure you have an eye on your luggage and have it locked under your Seats/Berths allocated to you.

Often the train stations may be very confusing as they are huge and very crowded especially in the big cities. Best to arrive early and engage an official porter (determine the price first) to not only carry your luggage to the platform, but they will also find where your seat is and take you there directly. If your porter is a good one they may also help in situations where you may find someone already in your booked seat. This can be money well spent and it is a good idea, if they give good service, to pay them a little extra as a tip (then they may also be willing to help the next foreigner who comes along).

Can I book the Train Tickets in Advance
Yes  you can book the Train tickets 60 days in advance (was 120 days)  (excluding day of journey) however for some short journey selected Trains it can be booked 30 days in Advance.  

Can I book the Train Tickets through Internet and Pay Online

It is exrodinarily difficult to book rail tickets for international travellers although not impossible!. The good news is that it's only a problem the first time. The procedure is detailed here:  The Man in Seat 61 

What are the different types of Trains
Basically for the long journey Trains you have Express & Super-fast Express Trains and the difference would a few hrs variation in the journey time.  Apart from the above Indian Railways also operate some Premium Trains called as Rajadhani Express and Shatabdi Express.  All of the Rajadhani & Shatabdi Trains have only AC accommodation and the Fare includes Snacks, Breakfast, Lunch, Dinner and the fare is on higher side by 35% compared to normal Express Trains.

Rajadhani Express runs from the Country Capital New Delhi to all State Capitals and the journey time varies between 12 to 36hrs depending upon the distance. 

Shatabdi Express are InterCity Trains covering max 6-8hrs one way journey and has only seat accommodation with two different AC classes.  For International Tourists  would strongly recommend Rajadhani / Shatabdi Express Trains if its available on the route you would like to travel.

New Series Duronto Express started in 2010:
  The Indian Railways started a new series of Express Trains called Duronto Express considered to be Non Stop Trains (though it would have Technical Halts for Crew Change but No Commercial Halts).  The Ticket Fare is a bit higher compared to normal Express Trains but still cheaper compared to Rajadhani Express and has Non AC & AC Sleeper Coaches.  Currently these trains are being introduced in a phased manner between different Metro Cities.  These Trains would reach the destinations 2-3 hrs earlier compared to the normal Express/Superfast Express Trains.

What are the different type of Travel Classes available
The long distance trains/overnight trains has the following options.
Sleeper Class           Non AC consisting of 6 berths in a block 
3AC  or Third AC       6 berths in a block / The best option
2AC  or Second AC  4 berths in a block / not worth the extra price

1AC or First AC          4 berths individual block with lockable door but Shared Toilets

*Bed Rolls consisting of Bedsheets, Blanket, Towel are provided in Overnight Trains in AC Coaches Only i.e. 1AC, 2AC, 3AC which are given around 8-9PM and collected back by 6AM

International Travellers avoid travelling in Sleeper Class
First AC is available only on selected Trains quite expensive on par with flight tickets rate.

The short distance trains which has only sitting accommodation has the following options.
Executive Chair Car      Available only in Shatabdi Express Trains
AC Chair Car                  Recommended
Second Sitting               Non AC basic Seats /  Avoid It.
(In case of Jan Shatabdi Express Trains you can travel by Second Sitting Class also)

Though it was mentioned not to Travel in Non-AC Coaches the exception would apply for JanShatabdi Express this has a Non AC Seat Accommodation and a bit comfortable and regular checking staff are available on the Train so unwanted people will not  occupy or share your seat.  JanShatabdi Trains are available in selected routes like Mumbai-Goa, Mumbai-Aurangabad, Kolkata-Bhubneshwar and some other routes.

I am confused and having trouble doing a Online Reservation from www.irctc.co.in website
Please Note that Indian Railways is the single largest network in the World and there are multiple Railway Stations within one City with different names.  For Example:  Agra has three Railway Stations which are Agra Cannt., Agra Fort, Agra City.  Due to various routes most of the Trains just pass trough one of the Railway Station and do not cover the other Railway Station within the same city. Follow the below steps while going trough the On-line Booking.

Once you are logged into www.irctc.co.in click on "Plan  Travel" once you see the Booking Form follow the instructions.

At the FROM field enter the Source/Boarding City/Town  and you need to click on the Icon beside the From Field (if you put the mouse over the Icon it says "Fetch Station Code"  This will list the Station Name.  If the respective City/Town has more than one Railway Station it will list the same and you need to select one and click on GO button. 

 At the TO field enter the Destination City/Town click on the Icon beside the Form Field and select relevant City/Town name click Go button.

Select Class from the drop-down as AC Chair for Day Journey Trains and for Overnight trains you need to select 1st Class, AC 2tier or AC 3tier or whatever relevant. Observed that people tried using AC Chair Car for overnight Trains and it never listed any trains.

Select E-ticket (Do not enable Tatkal) Click on Find Trains button.

You should see the Trains listed, see the timings and select which ever Trains suits you and click on Book ticket and follow the process.

If you do find multiple Railway Stations with the same City Name select one of them, and check for the Train List and if you don't find any trains being listed or the one you wanted to Travel, repeat the process selecting alternate Railway Station with the same City/Town Name.
For Example if you are trying to Book for a Train from New Delhi to Agra City or Agra Fort you will not find any Trains the reason being Trains coming from New Delhi do not touch Agra City/Fort Railway Stations and hence you need to select Agra Cantt.

What is the Luggage Limits and do ineed to Check-in
In AC class 40-45 kg per person is allowed, but anyhow as nobody checks the luggage and you will need to carry your luggage along with you while you travel you can carry even more and its no big deal as long you are not taking double your allowed limits.

Where is  Luggage stored?
You are supposed to put your luggage under your travel berths allocated to you for long journey trains and for short journey trains you need to put above where space is available.

Can I book the Train Tickets after reaching India
Most of the Trains travelling through the Tourist places have a specific quota like max. 4 berths for International Tourists but thats taking a chance further in major cities during the season it takes up to 2hrs for you to get through the Reservation Office.   As the bookings cannot be done on-line and 90 days in advance so book it online and have a pleasant journey.   Trains are the primary source of travel in India and people reserve normally one month in advance and for the peak season even much earlier.  The peak season for Trains in India would be January, April, May, September, October, December.    So always plan in advance for the Train journey.

Happy Journey.