How can I use my computer to get my Kid's birthday party invitations?

Your question isn't clear to me. Are you wishing to print some invitations that you'll then send out? If that is your desire, there are many software programs which make creating such things very simple.

Do you have email addresses of all the kids you wish to invite?
Or, are you asking if you can print out invitations on your computer.

You can do both.

Here's one for free: http://www.smilebox.com/lp/birthday-invitations-var3.html?partner=googleeu&campaign=search_us_birthday_invitation_nofree~birthday_invitation_party~&gclid=CJ_ml8j-xtACFVKIfgodHDkINg