This guide will have you doing Duolingo every day. For one to three days a week, you will need to invest 15 minutes on your phone. For the rest of the week, you will need to invest maybe 2 minutes or so. You are, of course, free to complete more lessons than necessary, which will make your XP and lingot gains even greater. You will not need Duo plus, although that would certainly make things easier.
If you are like me, you are very forgetful and need constant reminders. Set three alarms on your phone.
For the first alarm, set it for every day except Monday (very important, will explain later). If you are fine with being up at midnight, set it for midnight. Otherwise, set it for the earliest time before noon you're comfortable with. The exact time doesn't matter much, but I prefer earlier times because I forget about the alarm often. When you complete a lesson before noon local time, you get a 15-minute 2x XP boost that can be activated any time after 6 PM local time.
For the second alarm, set it for every sunday. The exact hour will depend on your time zone, and how long it would take for you to do a last-minute XP grind. If you live on the east coast of the US, and take as long as I do, set it for 9:30 PM. Personally, I choose this time for two reasons. First, outside daylight savings time, it gives me 30 mins of leeway in case I need to make up XP to stay in the league or top three or whatever my goal is.
For the third alarm, set it for every day. The best hour might vary by timezone and personal preference, but the idea of this alarm is governed by three factors. Remember that 2x XP boost we discussed earlier? We want to make use of that. So this alarm absolutely must be before midnight but after 6 PM. The second factor is that sometimes Duo has a "happy hour" at 7 PM (at least, 7 PM EST) where you get 2x XP for free. The third factor is that on Mondays, you begin a new league. Remember how we strangely didn't want to do duolingo on Monday mornings? It's because users who join leagues earlier in the day are generally more motivated to do Duolingo and thus get more XP, meaning if you start your league early you get stuck with super hardcore users who gain tons of XP and will probably make you lose the league. However, if we don't do ANY lessons today, we lose our streak, which we can't let happen. So we want to do the league as late as possible. Generally, in my experience, as long as you start the league after ~ 3 PM local time, you should be fine, but it is better to be safe than sorry! Personally, I set my alarm for 7 PM, but any time in the 6 PM - midnight interval works perfectly.
Different languages vary in lesson length. If you find it difficult to make enough time to do lessons, consider learning Swedish. For some reason, Legendary Reviews for Swedish only ask 1-3 questions on average. No, that's not a typo. Sometimes it literally does just ask one question, and you get 20 XP.
When your morning alarm goes off, do AT LEAST one lesson. Preferably, this should not be a gold or legendary review - save those for evenings. The XP you get from this lesson does not matter. You will be doing most of your work in the evening. Again, make sure you do NOT do any lessons Monday mornings, or you will get stuck with a difficult league.
If you currently have a gold-level topic, can access Duo on desktop, and do not plan on buying Duo plus, you should grind it to legendary status on desktop, because it is easier to get lingots (red gems for desktop duo) than gems (blue gems for mobile duo). Additionally, if your 'double or nothing' has run out, buy it again. Don't forget you can buy it on mobile AND desktop separately, and get the rewards for BOTH, even if you never do desktop lessons, only mobile ones!
During normal (not Sunday) evenings, watch your league position. If you want to maintain your current league, aim for a position between 15th and 20th. If you want to go to a higher league, aim for a position between 5th and 10th. These are fairly safe positions that do not require excessive XP grinding. If you are pressed for lingots/gems, do note, however, that the top 3 in any league get extra bonus gems. Do not aim for just above the demotion zone. Someone will snipe your position at the last minute and you will end up demoted.
Before doing your evening lessons, calculate how much XP you will need to get to the position you want. Compare it to how much XP you think you can get (If you have no idea how much you can get, read the XP section). Bear in mind any currently active bonuses. If that is not enough XP, and you are on mobile, purchase "perfect lesson boost" for 100 gems. This will double your XP, but only if you get every question correct - no misses. If you miss, consider restarting the lesson if you're less than half done.
As for lessons, you should do lessons in this order until you reach the league position you want:
Gold Review, Easy Legendary Review, and other options are not worth the time for the XP they give.
There are a few other things to note. You should make sure you have at least 4 legendary topics. If you have fewer than this, consider extra grinding (not on Monday, of course!) until you do. Ideally, you want as many as possible. I don't mean gold, either. Gold topics are the WORST possible topics because they give less XP than legendary ones.
If you do several perfect lessons in a row on a topic you're learning, Duo might ask you if you want to level up. Do not jump into this offer blindly; carefully consider it. You can get extra XP on the last lesson on a level. Additionally, if it would "upgrade" you to gold, but you can't afford legendary, definitely hold off until you can. I would only accept Duo's offer if I'm trying to grind a topic to legendary - otherwise, that's a hard pass from me.
Buy streak freezes whenever you can. Buy double-or-nothings whenever you can, on desktop AND mobile. Bear in mind, on desktop, every ten days, you get X free gems, where X is the number of days straight you've done duo, divided by ten. So, if you have a 200 day streak, you get 20 lingots/200 gems for free. Currently, I have a 977 day streak. This means that in three days I will get 98 free gems on desktop, and every week I get 20 more free gems from the two double-or-nothings I bought. that's over 12 lingots a day on desktop, average!