Great question! I've said it before and I'll say it again: Asia is growth and you cannot afford to not have an Asia growth strategy, regardless of the size of your company. I've been based here in Singapore for nearly 5 years and have observed how Singapore's leaders have worked hard to position Singapore as the regional hub in many industries, thus having a Singapore footprint is one the crucial steps in any company's strategy. Footprint can be anything from setting up a subsidiary company or finding the right type of local partner. The region presents tremendous opportunities but also offers a few challenges such as the diversity of its cultures and customs. Working with someone that knows the region and also has an international background is key. Having travelled the region (Vietnam, Malaysia, Thailand, Indonesia, Brunei, etc.) extensively and built a solid and trustworthy network, I'd be more than glad to support your expansion into the region. Do engage me here on the platform and provide me with more details about your business and what goals you'd like to achieve. In the meantime I encourage you to visit http://Singapore.fyi.to/InsightsfromtheInside where you can download a very special book on occasion of the SG50 celebrations where the Singapore International Federation partnered 50 individuals from around the world who have lived, visited, studied or worked in Singapore to share their stories about what makes Singapore tick, Singaporean idiosyncrasies, the surprises they found, and their involvements and contributions to the local community. My essay "What is There Not to Love about Singapore?" can be found on page 146.

The answer varies based on which country you are thinking of. If your focus is India or China, then the game is completely different to say Singapore.
I can speak for India, having spent last 5 years there in a sales overlay team and then in customer success. As a result I have seen both the selling side as well as the retention side.
Key things that come to my mind:
1) Product maturity - think scalability, availability
2) Pricing - think flexibility
3) Market - think not only competition but also how crowded it is
4) Customer service - think customer retention and ease of switching.
5) Selling - think size and local partner strategy.

A lot depends on what is your product, but this was my attempt to broadly identify some of the key things.

In both my roles in India, I faced challenges across all these areas and am happy to get on a call to discuss these in detail specific to your company and product.

This question needs way more details to be answered.
Some few things to explain why:

1-Countries in Asia are VERY different from each other. Chinese culture and Japanese are nothing alike. Business in each country is done on a completely different way

2-Depending on your industry, vertical and product, depends where you should go, and even if you knew where you would go, it may change your go-to market strategy

3-Growing in Asia is expensive (as more international expansion is) and requires lots of work up front so you don't lose all your money just going there.

This are just 3 of many other reasons (capital constrains, data jurisdiction, legal issues, company organizational needs, etc)

Asian countries act differently to an extent, once you understand that it will be easy for you. You can move cautiously with few countries and then apply it to the rest of the Asian countries. I will suggest you begin with East Asian Countries.
The East Asian experience more broadly, as illustrated by Japan, South Korea, and Taiwan, describes an economic development model with distinct policy objectives and institutional requirements at each stage. In fact, contrary to the prescriptions of free market economists, the East Asian model suggests that, especially in the early days of development, governments must sometimes judiciously intervene rather than simply liberalize their economies right away. The appeal of China’s autocratic political system to emerging countries’ elites is abundantly clear. Using the East Asian model as one potential development strategy, the first step is to implement household-based land redistribution programs and other productivity improvement initiatives, such as increasing irrigation and the use of fertilizer. It is easy to see why democracies are not necessarily advantaged during much of this long development trajectory, given the scope and complexity of the intervention required, the extractive nature of many policies, as well as the related need to overcome powerful vested interests. It is here where the comparison between democratic India and autocratic China is so instructive.
However, as economic convergence proceeds over time, democracy will likely regain its footing as the form of government best suited to deliver long-term growth in developed high-income economies. Either way, the key will be to abandon the prevailing orthodoxy that institutional change must invariably precede economic development, and focus instead on tailoring the degree, speed, and sequence of political and economic liberalization to the unique growth requirements of each emerging market.
You can read more here: https://www.strategy-business.com/blog/Lessons-from-the-East-Asian-Development-Model?gko=60f9c
Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath