Many flights connect India with Taipei from almost all international airports throughout the country. Many of these in fact go through New Delhi and is the only airport from where a direct route is available which is provided by China Airlines. Other airlines like Malaysian Airlines, Thai Airways, Singapore Airlines and others provide services on routes to Taipei.
Indian nationals can only apply for a Travel Authorisation Certificate if they already hold a valid resident or tourist visa or resident certificate issued by the USA, UK, Japan, Schengen countries, Australia, and New Zealand, and have not worked as a blue collar employee in Taiwan. If they do not meet these qualifications, they will not be permitted into the ROC (Taiwan).
Taipei's international airport, Taiwan Taoyuan International Airport, is fairly well-connected to all the continents and major countries in the world. The city also has another airport, the Songshan Airport which flies domestic routes and also international routes to nearby countries.
Taiwan has a great network of National Highways, Expressways and Provincial Highways, which connect towns and cities throughout the country to the capital of Taipei.
Rail connectivity in Taiwan is very good. Taipei is connected to all the major cities and towns via the HSR (high speed rail) and to others with the normal railways. The Taipei Railway Station is the main station in the city and all trains come here.
Local transport in Taipei is quite efficiently connected, much thanks to the MRT. This subway system connects the city very efficiently. The bus system is quite efficient too, though at first it might seem a bit complicated. Bus fares are consistent regardless of the distance. The best way to make your commute simple in Taipei is purchasing the EasyCard, which can be topped up and used in the MRT, the buses and even gives you discounts on a few stores. Taxis run throughout the city like anywhere else in the world. They can be hailed from the pavement and they are not very expensive.