Answer:

One of the most important things you can eat when trying to build yourself up is protein. Being a vegetarian is going to make it a little harder to get the protein you need to build your muscle but it definitely can be done.

Most of the higher-quality protein sources are animal-based (e.g. chicken, meat, fish, eggs, dairy, etc.) but there are certainly good sources of vegetable protein. These include soy (eat ONLY fermented soy, in the form of tofu), beans, etc.

If you're able to eat eggs, I would recommend you do that. Eggs are a very good source of high-quality protein.

In addition to protein, you're going to need to eat more calories in general. Basically that means eating more food. Exercise will give your body the push it needs to build muscle but it needs more food to be able to build that muscle. Focus on eating a LOT of calories during the day.

You can also consider vegan protein supplements to help with gaining weight.