if I have a font on my computer that doesn't say "Non-commercial use only" or something like that can I put it on web without a problem?
Unfortunately not. Web embedding is one use for which you'd need a separate, specific license.
Most times when you use a font, as long as you have the font file on your computer legally and are using it according to its license, you can do what you want with it.
However in the case of embedding the font as a web font, you are, according to the law, creating and distributing a derived version of the font file. This is because creating a web font from a desktop font on your computer means you're feeding the font file (which is protected by copyright) into a conversion process where it is converted into another format, and you are sharing that converted font file on the web.
Technically, when you upload a web font, you are giving anyone who visits your site the ability to download that font.
According to copyright law you would need to have explicit permission from the creator to do this, as it's not a permission that is granted by default - and it may be hard to argue fair use when making something available on the web.
In order to do this, you need a license which permits the creation and distribution of derivative works.
Web font licenses
Rather than give licenses which say "you can create and distribute derivative works", what font foundries tend to do is sell separate web font licenses which specifically apply to using them as a web font.
Web font licenses often come with conditions attached which specify the monthly number of page views your site is allowed to receive and still use the font, or it may even be sold on a subscription basis where you pay an ongoing fee.