How can I go about doing this? Google searches yield hundreds of ads for becoming ordained through different websites, but I am hesitant to trust any of them. I understand that different states have different rules, but there has to be a starting point that is non-religious and easier/less expensive than these google results.
I am guessing that you are asking this because you are interested in being an officiant at a marriage ceremony. There are many options, including the Church of Universal Life, for example. The legal question is what ordination is acceptable for the purpose for which you intend to use it.
Different states have different laws about who may officiate a wedding ceremony. It is important that you be certain you are permitted to do so with whatever ordination you are seeking. Although I believe there will be more litigation about this in years to come, not all states allow "internet ministers" to perform wedding ceremonies.
You may need to contact an attorney in the state to be sure, and this is advisable because marriages have very significant legal and property implications. You do not want a couple to have their marriage deemed void because you were the officiant in a state that does not allow that. This could affect everything from taxes to property ownership to the right to make medical decisions for each other.
As a general rule, tourist destinations and states with more secular populations are more likely to allow these marriages. I believe Pennsylvania also allows the couple to self-solemnize the ceremony, growing out of the customs of the Society of Friends.
The bottom line is that the answer is state-specific.