(Note: I am writing the response in an impersonal form only to make it generic across learners.)
I would break the problem down into three parts: awareness, learning the correct forms (conjugations) and using these forms in the appropriate context (the actual tenses).
Awareness here refers to what tenses are required most (i.e. not generally but by the learner). This information is useful in the interest of reducing the number of errors fast by tackling the most common errors first. In order to track the types of errors, you could use a type of journal, for example, with sentences containing errors and a note on the type of error (the time reference used, e.g. categorised as past, presence or future, and the tense that should have been used). After a while, it should become clear which area or tense needs to be tackled first.
(Journaling is not unusual in language learning—see for example Five Reasons You Should Write as Part of Your Language Learning—but the goal is usually not as specific as tracking errors in a specific area of usage.)
Learning the correct forms refers to the ability to build all the verb forms, not just the irregular forms, but also the regular ones and those that require auxiliary verbs. This is not a big deal in English, especially when compared with Spanish, French or even German. You can do this one tense at a time, based on the "importance" ranking of tenses that came out of the journaling activity.
Using the forms in the correct context obviously refers to using the tenses correctly. While this requires knowledge of the correct forms (see above), I don't consider this a separate step, but as something that should both reinforce and be reinforced by learning the correct forms. Of course, you need to know a few correct forms to start with, but this knowledge should be expanded by creating situations or dialogues where you need them.
For example, to practice the simple past, you can start conversations that require the simple past, e.g. talking about what someone did yesterday, on their honeymoon, during their last trip abroad, etc. When the learner makes an error, you can point out the correct form. To practice the simple future, you can start conversations about future plans, forecasts and predictions (the weather, stock prices, elections, ...), etc. (It gets trickier with more complex forms, such as those required by future progressive, but I am assuming that these tenses will come up less frequently.)
Of course, none of this excludes additional techniques, such as entering certain sentences as cloze tests into an SRS such as Anki, extensive reading, or a form of intensive reading where you underline or mark all instances of a specific tense in a piece of text (in order to collect examples and learn their patterns).