Garden lime is predominantly made up of calcium carbonate, which is ground-up limestone. Other liming materials include calcified seaweed, ground chalk, and ground magnesian limestone. These three will do just as good a job as classic garden lime and can be applied using the same method.
You can easily scatter this across your soil or dig it into the soil to establish it more. You can also do this as a 50/50 split, digging half into the soil, and then scattering the other half over the surface.
Another option is hydrated lime (calcium hydroxide), but you need to be a little more cautious when using this. It is very quick acting but may cause irritation to your skin or eyes, so use protective equipment whilst using.
To maintain this, mulch, and water your soil regularly. Alkaline soil tends to dry out quickly as it is chalkier, so by watering and retaining moisture your plants will be healthier.