How can I boost my Solo MMR in Dota 2?

There is only one way to gain MMR: through winning, as you might have thought. There currently is no other way (other than paying for a boost which is frowned upon) to do this, but there are some ways to give you a better chance at winning, therefore increasing your MMR indirectly.

1. Use meta Heros - dota 2 is a game where things are constantly balanced and changed so everything fits together. But things don't always go as planed, since Mr Icefrog can't crowd test every change and some Heros end up more powerful than others. As shown by this question, you can see blood seeker was an extremely OP hero in 6.86c, and recently in 6.85 Doom was the best due to the buff to his Scorched Earth ability. The best way to see what's good at the time is by going to the hero trends page on DotaBuff and sorting by current win rate.
2. Play as a team, don't put anyone down - Dota 2 is a team game, which means teamwork is key. I see too many times people lose just because they flame a teammate that didn't have a good game, or can't handle an aggressive tri-lane. If someone is feeding but you don't think it's on purpose, suggest them to farm the jungle instead of trying to farm lane, and make sure wards are up (more below) so they can see that they could be ganked.
3. Vision - Most people, especially in the lower brackets, will underestimate the role of the supports in a game. Supporting is probably one of the most crucial parts of Dota, even beyond the role of the carry. Supports make sure the team knows when to fall back because of spotting the enemy with a ward or when to engage into the rosh pit by surprise and wipe the enemy.
4. Communication - this is key. Some people are so focused on their lane they might not notice the enemy mid walking to them with a rune ward, so when you spot it call it out, either ping the enemy hero portrait and ping their lane or use the mic.

There are more ways, but these are some of the best options. Using these is likely to increase your chances of winning, therefore increasing your MMR overall

Judge2020's answer is good, but one huge difference you'll notice if you see any pro games is how good they are at farming. Last-hitting is a HUGE part of the game. You'll often see 50-60 plus last hits for the carries/mid lane at the 10 minute mark and this makes a huge difference - 50 last hits gets you somewhere around 2-2.3k gold depending on how many siege creeps you get etc.

Practice your last-hitting, using the ingame last-hit practice if necessary. Get good at it and get the timings down for like 5-10 heroes and you'll see a big uptick in your effectiveness. If you're playing support this still applies but you should ideally be denying in lane to stop the enemy's farm.