The easiest way would be to do this through your domain registrar (provided they offer this service). Domain forwarding/redirect can even utilize "URL Framing" where the link mysite2.com never changes no matter what page is being accessed on mysite1.com/sample
This can also be done through .HTACCESS provided you have mysite2.com hosted.
Since you have RegisterFly, and you want to enable "URL Framing," you must use the RegFly nameservers. This method is best if you don't want or need to host the domain yourself.
How long it takes depends because of internet caching (ie. your ISP). If you have never altered the default nameservers, it could happen instantly. I suppose 24-48hrs would be the "standard" answer but it will likely only take minutes or hours.
BONUS: With RegFly you can even use META tags. But this will not allow "framing," just redirect.
My favorite way is to utilize a cloned INDEX.HTML page that looks similar to my target page but with a timed META redirect.
When above is placed next to the <head> tag, it will send user to target site in 10 seconds.
Keep in mind, most 301's can effect your "PR" or search engines. There are folks on WHT that are masters at Page Ranking and I need to learn much from them. I have many domains just sitting there doing nada