It is indeed fairly simple, though you'll need to keep in mind the documentary requirements. You'll need the passport of the non-EU spouse and the passport or national ID card of the EU spouse. You'll also need proof of the relationship, which for spouses will normally be the marriage certificate.
The marriage certificate and other documents, if needed, may need to be authenticated depending on where they were issued. This is usually done by means of an apostille.
The governing EU legislation is Directive 2004/38/EC. The source you link to is incorrect on a few points. Most notably, it is not necessary for the non-EU spouse or partner to be economically dependent on the EU spouse or partner (Article 2, paragraph 2, items (a) and (b)).
Furthermore, it imprecisely states that the EU partner "must meet some financial criteria." In fact, the criteria are not necessarily financial. For example, if the EU spouse is employed in Spain, there are no financial requirements (Articles 7 and 8). Retired people, however, can indeed be asked to show that they can support themselves (Article 8, paragraph 3), but this can only be required before they acquire permanent residence (Article 16, paragraph 1).