Sex is considerably different than putting a tampon in your vagina. Normally you have sex after you have been sexually aroused for a while.
Sexual arousal means that a lot of blood pumped into your genitals, allowing them to heat up and open up. That will cause your vagina to lubricate with a slippery fluid called arousal fluid. This is plasma squeezed from the cells in your vaginal lining due to the vasocongestion (filling with blood). You will develop a desire to be touched and stroked and even penetrated during sexual arousal.
Sexual arousal also lifts your pain threshold considerable. So what will normally be painful, are perceived as pleasurable during arousal. The longer you are aroused, the more flexible the muscles becomes, allowing for easy and pleasant penetration.
If you want to make inserting a tampon easier, follow the instructions on how to stand. Make sure you are flowing enough so that the tampon does not go in dry. Use the smallest size you can that will fill up in 4 hours without leaking, use one with an plastic applicator. You can put some saliva or lubrication on the applicator to make it go in easier. Make sure you push the tampon all the way in, until you cannot feel it any more. If the tampon is too dry when you take it out, it will be painful. So use a lower absorbency or pads when your flow gets lighter. Remember to remove your last tampon.