If you want to take up fishing, perhaps on the river Tizsa, K-Fish Horgászcentrum is the shop for you. They stock plenty of fishing tackle.
If you want to fish in Budapest on the river Danube, in Szeged on the river Tízsa, or on local lakes around Hungary (such as Lake Balaton and Lake Velence), you will need a State (Hungarian) Fishing License and a Local (i.e. Budapest or Szeged) Fishing License; regardless if you are a Hungarian or "Foreigner".
A State (Hungarian) Fishing License can be bought from a fishing club, such as the Szeged Fishing Association or Hungarian National Fishing Association, once you are a registred member of that fishing club. However, if you already have a Fishing License from your own country it can be used in place of a Hungarian State Fishing License. Either way, you must then purchase a Local Fishing License; usually from a fishing shop or the waterway keeper of the lake or river you are interested in fishing on.
Lake Vértó, Szeged - The shed is where you can buy a daily fishing license
A Hungarian State Fishing License is valid for one year, from January 1st until December 31st, and currently costs 8,500 HUF (£22.66) per year; in Szeged at least. Before being granted a Hungarian State Fishing License though, you will need to past a small exam about Fishing Regulations and so on - Just take a Hungarian friend along to help with translation, etc.
With the Local Fishing License (bought from K-Fish for example): If you are just using a specific lake or river all year around, you are better off paying for its yearly license. And if you use individual lakes or rivers all year around, you are better off paying for their daily license. A daily license in Szeged (lake Vértó) costs 2,800 HUF (£7.46) and a yearly license costs 16,000 HUF (£42.66). You can take the fish you caught home.
NOTE: As a fishing member you must keep a log book that contains a record of each and every fish you catch throughout the year. The log book needs to be submitted pending renewal of your new Hungarian State Fishing License.
If you are fishing on angler-used waters as an adult angler, you may use two fishing rods at the same time. And if you are fishing on angler-used waters as a junior angler (under 18 years), you may only use one fishing rod at a time. On other types of waterways you can usually use two rods at a time. A child angler (under 14 years) can only angle with one rod at any place. Besides the number of fishing rods, only one piece of 'live-bait square fishing net', smaller than 1 Square Meter, can be used.
The minimal body length that can be fished, indicated on the angling ticket, refers to the distance between the peak of the nose and the beginning of the tail fin (i.e. It is not the total body length but the length of the trunk). The state angling ticket also indicates the period when angling is prohibited for each fish species in detail.
The closing season may be altered on some waters rendering legal regulations more strict or alleviating them based on local features and state permissions. More information can be found at your local fishing club and on the above websites.